Professor Gus Lehrer

F07 - Carslaw Building
The University of Sydney

Telephone 9351 2977
Fax 9351 4534

Research interests

Algebraic and geometric aspects of representation theory; reductive algebraic groups, particularly over finite fields; Algebraic geometry, spaces of configurations in algebraic varieties; Hecke and other algebras. Cohomological group actions; Knot-theoretic algebra, including diagram algebras and braid groups.

Gus Lehrer is a member of the Algebra Research Group.

Teaching and supervision

Timetable

Current research students

Project title Research student
Braided tensor categories, cellularity and diagrammatics in invariant theory Yang Zhang ZHANG

Selected grants

2016

  • Algebraic Schubert geometry and unitary reflection groups; Lehrer G, Henderson A; Australian Research Council (ARC)/Discovery Projects (DP).

2015

  • Symmetry via braiding, diagrammatics and cellularity; Lehrer G, Zhang R; Australian Research Council (ARC)/Discovery Projects (DP).

2012

  • Quantised algebras, supersymmetry and invariant theory; Lehrer G, Zhang R; Australian Research Council (ARC)/Discovery Projects (DP).

2011

  • Flag varieties and configuration spaces in algebra; Lehrer G; Australian Research Council (ARC)/Discovery Projects (DP).

2007

  • Invariant theory, cellularity and geometry.; Lehrer G, Zhang R; Australian Research Council (ARC)/Discovery Projects (DP).

2005

  • Geometric structures in representation theory; Lehrer G; Australian Research Council (ARC)/Discovery Projects (DP).

2001

  • Geometric themes in the representation theory of groups and algebras; Lehrer G; Australian Research Council (ARC)/Large Research Grants (LRG).

2000

  • Group representation theory and cohomology of algebraic varieties; Lehrer G; Australian Research Council (ARC)/Large Research Grants (LRG).
  • Geometric aspects of the representation theory of algebraic structures; Lehrer G; Australian Research Council (ARC)/Australian Senior Research Fellowship.

Selected publications

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Books

  • Lehrer, G., Taylor, D. (2009). Unitary Reflection Groups. United States of America: Cambridge University Press.

Book Chapters

  • Lehrer, G., Zhang, R. (2010). A Temperley-Lieb Analogue for the BMW Algebra. In A Gyoja, H Nakajima, K Shinoda, T Shoji, T Tanisaki (Eds.), Representation Theory of Algebraic Groups and Quantum Groups, (pp. 155-190). New York: Birkhauser (imprint of Springer).
  • Lehrer, G. (2002). Geometric themes in representation theory (in Chinese). Algebra in the 21st Century, (pp. 33-49). Beijing: Beijing University Press.

Journals

  • Lehrer, G., Zhang, R. (2017). The First Fundamental Theorem of Invariant Theory for the Orthosymplectic Supergroup. Communications in Mathematical Physics, 349(2), 661-702. [More Information]
  • Andersen, H., Lehrer, G., Zhang, R. (2015). Cellularity of certain quantum endomorphism algebras. Pacific Journal of Mathematics, 279(1), 11-35. [More Information]
  • Lehrer, G., Zhang, R. (2015). The Brauer category and invariant theory. Journal of the European Mathematical Society, 17(9), 2311-2351. [More Information]
  • Digne, F., Lehrer, G., Michel, J. (2014). On character sheaves and characters of reductive groups at unipotent classes. Pure and Applied Mathematics Quarterly, 10(3), 459-512. [More Information]
  • Lehrer, G., Zhang, R. (2012). Quantum group actions on rings and equivariant K-theory. Contemporary Mathematics, 565, 115-141. [More Information]
  • Lehrer, G., Zhang, R. (2012). The second fundamental theorem of invariant theory for the orthogonal group. Annals of Mathematics, 176(3), 2031-2054. [More Information]
  • Lehrer, G., Zhang, H., Zhang, R. (2011). A Quantum Analogue of the First Fundamental Theorem of Classical Invariant Theory. Communications in Mathematical Physics, 301, 131-174. [More Information]
  • Lehrer, G., Nakano, D., Zhang, R. (2011). Detecting cohomology for Lie superalgebras. Advances in Mathematics, 228(4), 2098-2115. [More Information]
  • Dyer, M., Lehrer, G. (2011). Reflection subgroups of finite and affine Weyl groups. Transactions of the American Mathematical Society, 363(11), 5971-6005. [More Information]
  • Dyer, M., Lehrer, G. (2011). Root subsystems of loop extensions. Transformation Groups, 16(3), 767-781. [More Information]
  • Henderson, A., Lehrer, G. (2009). The equivariant Euler characteristic of real Coxeter toric varieties. Bulletin of the London Mathematical Society, 41(3), 515-523. [More Information]
  • Lehrer, G., Zhang, R. (2008). On Endomorphisms of Quantum Tensor Space. Letters in Mathematical Physics, 86, 209-227. [More Information]
  • Lehrer, G. (2008). Rational points and Coxeter group actions on the cohomology of toric varieties. Annales de l'Institut Fourier, 58(2), 671-688.
  • Lehrer, G., van Hamel, J. (2007). Euler characteristics of the real points of certain varieties of algebraic tori. Proceedings of the London Mathematical Society, 94(3), 715-748. [More Information]
  • Kisin, M., Lehrer, G. (2006). Eigenvalues of Frobenius and Hodge numbers. Pure and Applied Mathematics Quarterly, 2(2), 497-518.
  • Lehrer, G., Zhang, R. (2006). Strongly multiplicity free modules for Lie algebras and quantum groups. Journal of Algebra, 306(1), 138-174. [More Information]
  • Bonnafe, C., Lehrer, G., Michel, J. (2006). Twisted invariant theory for reflection groups. Nagoya Mathematical Journal, 182, 135-170.
  • Lehrer, G. (2005). Remarks concerning linear characters of reflection groups. Proceedings of the American Mathematical Society, 133(11), 3163-3169.
  • Lehrer, G. (2004). A New Proof Of Steinberg's Fixed-Point Theorem. International Mathematics Research Notices, 2004 (28), 1407-1411.
  • Lehrer, G. (2004). Generalised Euler Characteristics of Varieties of Tori in Lie Groups. Resenhas do Instituto de Matematica e Estatistica da Universidade de Sao Paulo, 6, 257-264.
  • Lehrer, G. (2004). Rational Points And Cohomology Of Discriminant Varieties. Advances in Mathematics, 186(1), 229-250.
  • Graham, J., Lehrer, G. (2003). Diagram algebras, Hecke algebras and decomposition numbers at roots of unity. Annales Scientifiques de lEcole Normale Superieure, 36(4), 479-524.
  • Lehrer, G., Michel, J. (2003). Invariant theory and eigenspaces for unitary reflection groups. Academie des Sciences. Comptes Rendus. Mathematique, 336(10), 795-800.
  • Digne, F., Lehrer, G., Michel, J. (2003). The space of unipotently supported class functions on a finite reductive group. Journal of Algebra, 260(1), 111-137.
  • Kisin, M., Lehrer, G. (2002). Equivariant Poincare polynomials and counting points over finite fields. Journal of Algebra, 247, 435-451. [More Information]
  • Graham, J., Lehrer, G. (2002). The two-step nilpotent representations of the extended affine Hecke algebra of type A. Compositio Mathematica, 133, 173-197.
  • Blair, J., Lehrer, G. (2001). Cohomology actions and centralisers in unitary reflection groups. Proceedings of the London Mathematical Society, 83(3), 582-604.
  • Lehrer, G., Segal, G. (2001). Homology stability for classical regular semisimple varieties. Mathematische Zeitschrift, 236(2), 251-290.
  • Lehrer, G., Xi, N. (2001). On the injectivity of the Braid group in the Hecke algebra. Bulletin of the Australian Mathematical Society, 64, 487-493.
  • Lehrer, G. (2000). Equivariant cohomology of configurations in Rn. Algebras and Representation Theory, 3, 373-384.

Conferences

  • Dimca, A., Lehrer, G. (2012). Hodge-Deligne equivariant polynomials and monodromy of hyperplane arrangements. Configuration Spaces: Geometry, Combinatorics and Topology, Pisa: Scuola normale superiore di Pisa.
  • Graham, J., Lehrer, G. (2004). Cellular Algebras And Diagram Algebras In Representation Theory. Mathematical Society of Japan's 10th International Conference : Representation Theory of Algebraic Groups and Quantum Groups, Tokyo, Japan: Mathematical Society of Japan.

2017

  • Lehrer, G., Zhang, R. (2017). The First Fundamental Theorem of Invariant Theory for the Orthosymplectic Supergroup. Communications in Mathematical Physics, 349(2), 661-702. [More Information]

2015

  • Andersen, H., Lehrer, G., Zhang, R. (2015). Cellularity of certain quantum endomorphism algebras. Pacific Journal of Mathematics, 279(1), 11-35. [More Information]
  • Lehrer, G., Zhang, R. (2015). The Brauer category and invariant theory. Journal of the European Mathematical Society, 17(9), 2311-2351. [More Information]

2014

  • Digne, F., Lehrer, G., Michel, J. (2014). On character sheaves and characters of reductive groups at unipotent classes. Pure and Applied Mathematics Quarterly, 10(3), 459-512. [More Information]

2012

  • Dimca, A., Lehrer, G. (2012). Hodge-Deligne equivariant polynomials and monodromy of hyperplane arrangements. Configuration Spaces: Geometry, Combinatorics and Topology, Pisa: Scuola normale superiore di Pisa.
  • Lehrer, G., Zhang, R. (2012). Quantum group actions on rings and equivariant K-theory. Contemporary Mathematics, 565, 115-141. [More Information]
  • Lehrer, G., Zhang, R. (2012). The second fundamental theorem of invariant theory for the orthogonal group. Annals of Mathematics, 176(3), 2031-2054. [More Information]

2011

  • Lehrer, G., Zhang, H., Zhang, R. (2011). A Quantum Analogue of the First Fundamental Theorem of Classical Invariant Theory. Communications in Mathematical Physics, 301, 131-174. [More Information]
  • Lehrer, G., Nakano, D., Zhang, R. (2011). Detecting cohomology for Lie superalgebras. Advances in Mathematics, 228(4), 2098-2115. [More Information]
  • Dyer, M., Lehrer, G. (2011). Reflection subgroups of finite and affine Weyl groups. Transactions of the American Mathematical Society, 363(11), 5971-6005. [More Information]
  • Dyer, M., Lehrer, G. (2011). Root subsystems of loop extensions. Transformation Groups, 16(3), 767-781. [More Information]

2010

  • Lehrer, G., Zhang, R. (2010). A Temperley-Lieb Analogue for the BMW Algebra. In A Gyoja, H Nakajima, K Shinoda, T Shoji, T Tanisaki (Eds.), Representation Theory of Algebraic Groups and Quantum Groups, (pp. 155-190). New York: Birkhauser (imprint of Springer).

2009

  • Henderson, A., Lehrer, G. (2009). The equivariant Euler characteristic of real Coxeter toric varieties. Bulletin of the London Mathematical Society, 41(3), 515-523. [More Information]
  • Lehrer, G., Taylor, D. (2009). Unitary Reflection Groups. United States of America: Cambridge University Press.

2008

  • Lehrer, G., Zhang, R. (2008). On Endomorphisms of Quantum Tensor Space. Letters in Mathematical Physics, 86, 209-227. [More Information]
  • Lehrer, G. (2008). Rational points and Coxeter group actions on the cohomology of toric varieties. Annales de l'Institut Fourier, 58(2), 671-688.

2007

  • Lehrer, G., van Hamel, J. (2007). Euler characteristics of the real points of certain varieties of algebraic tori. Proceedings of the London Mathematical Society, 94(3), 715-748. [More Information]

2006

  • Kisin, M., Lehrer, G. (2006). Eigenvalues of Frobenius and Hodge numbers. Pure and Applied Mathematics Quarterly, 2(2), 497-518.
  • Lehrer, G., Zhang, R. (2006). Strongly multiplicity free modules for Lie algebras and quantum groups. Journal of Algebra, 306(1), 138-174. [More Information]
  • Bonnafe, C., Lehrer, G., Michel, J. (2006). Twisted invariant theory for reflection groups. Nagoya Mathematical Journal, 182, 135-170.

2005

  • Lehrer, G. (2005). Remarks concerning linear characters of reflection groups. Proceedings of the American Mathematical Society, 133(11), 3163-3169.

2004

  • Lehrer, G. (2004). A New Proof Of Steinberg's Fixed-Point Theorem. International Mathematics Research Notices, 2004 (28), 1407-1411.
  • Graham, J., Lehrer, G. (2004). Cellular Algebras And Diagram Algebras In Representation Theory. Mathematical Society of Japan's 10th International Conference : Representation Theory of Algebraic Groups and Quantum Groups, Tokyo, Japan: Mathematical Society of Japan.
  • Lehrer, G. (2004). Generalised Euler Characteristics of Varieties of Tori in Lie Groups. Resenhas do Instituto de Matematica e Estatistica da Universidade de Sao Paulo, 6, 257-264.
  • Lehrer, G. (2004). Rational Points And Cohomology Of Discriminant Varieties. Advances in Mathematics, 186(1), 229-250.

2003

  • Graham, J., Lehrer, G. (2003). Diagram algebras, Hecke algebras and decomposition numbers at roots of unity. Annales Scientifiques de lEcole Normale Superieure, 36(4), 479-524.
  • Lehrer, G., Michel, J. (2003). Invariant theory and eigenspaces for unitary reflection groups. Academie des Sciences. Comptes Rendus. Mathematique, 336(10), 795-800.
  • Digne, F., Lehrer, G., Michel, J. (2003). The space of unipotently supported class functions on a finite reductive group. Journal of Algebra, 260(1), 111-137.

2002

  • Kisin, M., Lehrer, G. (2002). Equivariant Poincare polynomials and counting points over finite fields. Journal of Algebra, 247, 435-451. [More Information]
  • Lehrer, G. (2002). Geometric themes in representation theory (in Chinese). Algebra in the 21st Century, (pp. 33-49). Beijing: Beijing University Press.
  • Graham, J., Lehrer, G. (2002). The two-step nilpotent representations of the extended affine Hecke algebra of type A. Compositio Mathematica, 133, 173-197.

2001

  • Blair, J., Lehrer, G. (2001). Cohomology actions and centralisers in unitary reflection groups. Proceedings of the London Mathematical Society, 83(3), 582-604.
  • Lehrer, G., Segal, G. (2001). Homology stability for classical regular semisimple varieties. Mathematische Zeitschrift, 236(2), 251-290.
  • Lehrer, G., Xi, N. (2001). On the injectivity of the Braid group in the Hecke algebra. Bulletin of the Australian Mathematical Society, 64, 487-493.

2000

  • Lehrer, G. (2000). Equivariant cohomology of configurations in Rn. Algebras and Representation Theory, 3, 373-384.

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