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

Selected grants

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

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

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. (2012). Quantum group actions on rings and equivariant K-theory. Contemporary Mathematics, 565, 115-141.
  • 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.
  • 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 l'Ecole 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.

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.
  • 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.
  • 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 l'Ecole 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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