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.
Timetable
Selected publications
Unitary Reflection Groups
(Cambridge University Press, 2009)
Publications
Expand all
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). [More Information]
- 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, Y. (2024). Milnor fibre homology complexes. Pure and Applied Mathematics Quarterly, 20 Open Access(3), 1371-1431. [More Information]
- Lehrer, G., Lyu, M. (2023). Generalised Temperley-Lieb algebras of type G(r,1,n). Journal of Pure and Applied Algebra, 227 (Open Access)(10), Article 107402 - 1-Article 107402 - 36. [More Information]
- Iohara, K., Lehrer, G., Zhang, R. (2021). EQUIVALENCE OF A TANGLE CATEGORY AND A CATEGORY OF INFINITE DIMENSIONAL Uq (sl2)-MODULES. Representation Theory, 25(10), 265-299. [More Information]
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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. [More Information]
- 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.
Expand all
2024
- Lehrer, G., Zhang, Y. (2024). Milnor fibre homology complexes. Pure and Applied Mathematics Quarterly, 20 Open Access(3), 1371-1431. [More Information]
2023
- Lehrer, G., Lyu, M. (2023). Generalised Temperley-Lieb algebras of type G(r,1,n). Journal of Pure and Applied Algebra, 227 (Open Access)(10), Article 107402 - 1-Article 107402 - 36. [More Information]
2021
- Iohara, K., Lehrer, G., Zhang, R. (2021). EQUIVALENCE OF A TANGLE CATEGORY AND A CATEGORY OF INFINITE DIMENSIONAL Uq (sl2)-MODULES. Representation Theory, 25(10), 265-299. [More Information]
- Lehrer, G., Zhang, R. (2021). The Second Fundamental Theorem Of Invariant Theory For The Orthosymplectic Supergroup. Nagoya Mathematical Journal, 242, 52-76. [More Information]
2020
- Lehrer, G. (2020). A factorisation theorem for the coinvariant algebra of a unitary reflection group. Archiv der Mathematik, 114(6), 631-639. [More Information]
- Lehrer, G., Zhang, H., Zhang, R. (2020). First fundamental theorems of invariant theory for quantum supergroups. European Journal of Mathematics, 6(3), 928-976. [More Information]
2019
- Dyer, M., Lehrer, G. (2019). Geometry of certain finite Coxeter group actions. Proceedings of the London Mathematical Society, 118(2), 351-378. [More Information]
- Iohara, K., Lehrer, G., Zhang, R. (2019). Temperley-Lieb algebras at roots of unity, a fusion category and the Jones quotient. Mathematical Research Letters, 26(1), 121-158. [More Information]
2018
- Dyer, M., Lehrer, G. (2018). Parabolic subgroup orbits on finite root systems. Journal of Pure and Applied Algebra, 222(12), 3849-3857. [More Information]
- Deligne, P., Lehrer, G., Zhang, R. (2018). The first fundamental theorem of invariant theory for the orthosymplectic super group. Advances in Mathematics, 327, 4-24. [More Information]
2017
- Lehrer, G., Zhang, R. (2017). Invariants of the orthosymplectic Lie superalgebra and super Pfaffians. Mathematische Zeitschrift, 286, 893-917. [More Information]
- Lehrer, G., Zhang, R. (2017). Invariants of the special orthogonal group and an enhanced Brauer category. L'Enseignement Mathematique, 63(1-2), 181-200. [More Information]
- Srinivasan, B., Collins, M., Lehrer, G. (2017). Special issue in memory of Professor James Alexander ("Sandy) Green. Journal of Algebra, 475, 1-3. [More Information]
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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. [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]
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]
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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). [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]
- 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. [More Information]
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. [More Information]
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.
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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. [More Information]
- Lehrer, G., Michel, J. (2003). Invariant theory and eigenspaces for unitary reflection groups. Academie des Sciences. Comptes Rendus. Mathematique, 336(10), 795-800. [More Information]
- 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. [More Information]
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. [More Information]
2001
- Blair, J., Lehrer, G. (2001). Cohomology actions and centralisers in unitary reflection groups. Proceedings of the London Mathematical Society, 83(3), 582-604. [More Information]
- 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.
Selected Grants
2025
- Algebraic Schubert geometry and unitary reflection groups, Lehrer G, Henderson A, Williamson G, 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)
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