Associate Professor Anthony Henderson

F07 - Carslaw Building
The University of Sydney

Telephone 9351 3881
Fax 9351 4534

Website Personal web page

Research interests

I am a member of the Algebra research group. Broadly speaking, I am interested in geometric and combinatorial aspects of representation theory. In particular, I have a long-standing interest in the geometry of nilpotent varieties and Springer fibres, and their generalizations such as orbit closures in Hilbert nullcones and Nakajima's quiver varieties. It is often the case that the (intersection) cohomology of these varieties controls decomposition numbers in representation theory.

Teaching and supervision

Timetable

Awards and honours

2012: Medal of the Australian Mathematical Society

2011: Christopher Heyde Medal of the Australian Academy of Science, for research in the mathematical sciences

2009: Faculty of Science Citation for excellence in teaching

Selected grants

2013

  • Connections between geometry, combinatorics and representation theory; Stapledon A, Stapledon A, Henderson A; DVC Research/Postdoctoral Research Fellowship Scheme.

2012

  • Springer fibres, nilpotent cones, and representation theory; Henderson A; Australian Research Council (ARC)/Future Fellowships (FT).

2009

  • The geometry of exotic nilpotent cones; Henderson A; Australian Research Council (ARC)/Discovery Projects (DP).
  • Pyramids and decomposition numbers for the symmetric and general linear groups; Mathas A, Henderson A; Australian Research Council (ARC)/Discovery Projects (DP).

2003

  • Canonical bases for standard modules of affine Hecke algebras; Australian Research Council (ARC)/Australian Laureate Fellowships (FL).

Selected publications

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Books

  • Henderson, A. (2012). Representations of Lie Algebras An Introduction Through gln. UK: Cambridge University Press.

Journals

  • Achar, P., Henderson, A. (2013). Geometric Satake, Springer correspondence and small representations. Selecta Mathematica - New Series, 19(4), 949-986. [More Information]
  • Henderson, A., Trapa, P. (2012). The exotic Robinson-Schensted correspondence. Journal of Algebra, 370(2012), 32-45.
  • Henderson, A., Wachs, M. (2012). Unimodality of Eulerian quasisymmetric functions. Journal of Combinatorial Theory, Series A, 119, 135-145. [More Information]
  • Achar, P., Henderson, A. (2011). Corrigendum to "Orbit closures in the enhanced nilpotent cone". Advances in Mathematics, 228(5), 2984-2988. [More Information]
  • Henderson, A. (2011). Enhancing the Jordan Canonical Form. Gazette of the Australian Mathematical Society, 38(4), 206-211.
  • Achar, P., Henderson, A., Jones, B. (2011). Normality of orbit closures in the enhanced nilpotent cone. Nagoya Mathematical Journal, 203, 1-45. [More Information]
  • Achar, P., Henderson, A., Sommers, E. (2011). Pieces of nilpotent cones for classical groups. Representation Theory, 15, 584-616. [More Information]
  • Henderson, A. (2010). Exterior powers of the reflection representation in the cohomology of Springer fibres. Academie des Sciences. Comptes Rendus. Mathematique, 348(19-20), 1055-1058. [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]
  • Achar, P., Henderson, A. (2008). Orbit closures in the enhanced nilpotent cone. Advances in Mathematics, 219(1), 27-62. [More Information]
  • Henderson, A., Rains, E. (2008). The cohomology of real De Concini-Procesi models of Coxeter type. International Mathematics Research Notices, 2008, rnn001-1-rnn001-29. [More Information]
  • Henderson, A. (2008). The symmetric group representation on cohomology of the regular elements of a maximal torus of the special linear group. Journal of the Australian Mathematical Society, 84, 85-98.
  • Henderson, A. (2007). Induced characters of the projective general linear group over a finite field. Journal of Algebra, 307(1), 116-135. [More Information]
  • Henderson, A. (2007). Nilpotent orbits of linear and cyclic quivers and Kazhdan-Lusztig polynomials of type A. Representation Theory, 11, 95-121.
  • Henderson, A. (2006). Bases for certain cohomology representations of the symmetric group. Journal of Algebraic Combinatorics, 24(4), 361-390. [More Information]
  • Henderson, A. (2006). Plethysm for wreath products and homology of sub-posets of Dowling lattices. The Journal of Combinatorics, 13, 1-25.
  • Henderson, A. (2005). Species over a finite field. Journal of Algebraic Combinatorics, 21(2), 147-161. [More Information]
  • Henderson, A. (2004). Representations of wreath products on cohomology of De Concini-Procesi compactifications. International Mathematics Research Notices, 2004 (20), 983-1021.
  • Henderson, A. (2003). Symmetric subgroup invariants in irreducible representations of GF, when G=GLn. Journal of Algebra, 261(1), 102-144.
  • Henderson, A. (2003). Two-row nilpotent orbits of cyclic quivers. Mathematische Zeitschrift, 243, 127-143. [More Information]
  • Henderson, A. (2001). Fourier transform, parabolic induction, and nilpotent orbits. Transformation Groups, 6(4), 353-370.
  • Henderson, A. (2001). Spherical functions of the symmetric space G(F_q2)/G(F_q). Representation Theory, 5, 581-614.

Conferences

  • Henderson, A. (2012). Rational cohomology of the real Coxeter toric variety of type A. Configuration Spaces: Geometry, Combinatorics and Topology, Pisa: Scuola normale superiore di Pisa.

2013

  • Achar, P., Henderson, A. (2013). Geometric Satake, Springer correspondence and small representations. Selecta Mathematica - New Series, 19(4), 949-986. [More Information]

2012

  • Henderson, A. (2012). Rational cohomology of the real Coxeter toric variety of type A. Configuration Spaces: Geometry, Combinatorics and Topology, Pisa: Scuola normale superiore di Pisa.
  • Henderson, A. (2012). Representations of Lie Algebras An Introduction Through gln. UK: Cambridge University Press.
  • Henderson, A., Trapa, P. (2012). The exotic Robinson-Schensted correspondence. Journal of Algebra, 370(2012), 32-45.
  • Henderson, A., Wachs, M. (2012). Unimodality of Eulerian quasisymmetric functions. Journal of Combinatorial Theory, Series A, 119, 135-145. [More Information]

2011

  • Achar, P., Henderson, A. (2011). Corrigendum to "Orbit closures in the enhanced nilpotent cone". Advances in Mathematics, 228(5), 2984-2988. [More Information]
  • Henderson, A. (2011). Enhancing the Jordan Canonical Form. Gazette of the Australian Mathematical Society, 38(4), 206-211.
  • Achar, P., Henderson, A., Jones, B. (2011). Normality of orbit closures in the enhanced nilpotent cone. Nagoya Mathematical Journal, 203, 1-45. [More Information]
  • Achar, P., Henderson, A., Sommers, E. (2011). Pieces of nilpotent cones for classical groups. Representation Theory, 15, 584-616. [More Information]

2010

  • Henderson, A. (2010). Exterior powers of the reflection representation in the cohomology of Springer fibres. Academie des Sciences. Comptes Rendus. Mathematique, 348(19-20), 1055-1058. [More Information]

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]

2008

  • Achar, P., Henderson, A. (2008). Orbit closures in the enhanced nilpotent cone. Advances in Mathematics, 219(1), 27-62. [More Information]
  • Henderson, A., Rains, E. (2008). The cohomology of real De Concini-Procesi models of Coxeter type. International Mathematics Research Notices, 2008, rnn001-1-rnn001-29. [More Information]
  • Henderson, A. (2008). The symmetric group representation on cohomology of the regular elements of a maximal torus of the special linear group. Journal of the Australian Mathematical Society, 84, 85-98.

2007

  • Henderson, A. (2007). Induced characters of the projective general linear group over a finite field. Journal of Algebra, 307(1), 116-135. [More Information]
  • Henderson, A. (2007). Nilpotent orbits of linear and cyclic quivers and Kazhdan-Lusztig polynomials of type A. Representation Theory, 11, 95-121.

2006

  • Henderson, A. (2006). Bases for certain cohomology representations of the symmetric group. Journal of Algebraic Combinatorics, 24(4), 361-390. [More Information]
  • Henderson, A. (2006). Plethysm for wreath products and homology of sub-posets of Dowling lattices. The Journal of Combinatorics, 13, 1-25.

2005

  • Henderson, A. (2005). Species over a finite field. Journal of Algebraic Combinatorics, 21(2), 147-161. [More Information]

2004

  • Henderson, A. (2004). Representations of wreath products on cohomology of De Concini-Procesi compactifications. International Mathematics Research Notices, 2004 (20), 983-1021.

2003

  • Henderson, A. (2003). Symmetric subgroup invariants in irreducible representations of GF, when G=GLn. Journal of Algebra, 261(1), 102-144.
  • Henderson, A. (2003). Two-row nilpotent orbits of cyclic quivers. Mathematische Zeitschrift, 243, 127-143. [More Information]

2001

  • Henderson, A. (2001). Fourier transform, parabolic induction, and nilpotent orbits. Transformation Groups, 6(4), 353-370.
  • Henderson, A. (2001). Spherical functions of the symmetric space G(F_q2)/G(F_q). Representation Theory, 5, 581-614.

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