THE SECOND FUNDAMENTAL THEOREM OF INVARIANT THEORY FOR THE ORTHOSYMPLECTIC SUPERGROUP

Autor: R. B. Zhang, Gus Lehrer

Publikováno v: Nagoya Mathematical Journal. 242:52-76

The first fundamental theorem of invariant theory for the orthosymplectic supergroup scheme $\text{OSp}(m|2n)$ states that there is a full functor from the Brauer category with parameter $m-2n$ to the category of tensor representations of $\text{OSp}

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::4cc3e1d5524465e7c580008ea7448a65
https://doi.org/10.1017/nmj.2019.25

Temperley-Lieb Algebras At Roots of Unity, A Fusion category and the Jones Quotient

Autor: Kenji Iohara, Gus Lehrer, Ruibin Zhang

Publikováno v: Mathematical Research Letters
Mathematical Research Letters, 2019, 26 (1), pp.121-158. ⟨10.4310/mrl.2019.v26.n1.a8⟩

When the parameter $q$ is a root of unity, the Temperley-Lieb algebra $\TL_n(q)$ is non-semisimple for almost all $n$. In this work, using cellular methods, we give explicit generating functions for the dimensions of all the simple $\TL_n(q)$-modules

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c10bef39d08b9eb7428ac76085cdd305
https://hal.archives-ouvertes.fr/hal-01476831v3/file/ILZ.pdf

Cohomology of the Milnor Fibre of a Hyperplane Arrangement with Symmetry

Autor: Gus Lehrer, Alexandru Dimca

Publikováno v: Springer INdAM Series ISBN: 9783319315799
Configuration Spaces
Configuration Spaces, Geometry, Combinatorics and Topology
Configuration Spaces, Geometry, Combinatorics and Topology, 2015, Cortona, Italy. pp.319-360, ⟨10.1007/978-3-319-31580-5_10⟩

We prove some general results concerning the cohomology of the Milnor fibre of a hyperplane arrangement, and apply them to the case when the arrangement has some symmetry properties, particularly the case of the set of reflecting hyperplanes of a uni

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bec7ed1481dfa3f789762c9617c127aa
https://doi.org/10.1007/978-3-319-31580-5_10

Poincar� polynomials for unitary reflection groups

Autor: Gus Lehrer

Publikováno v: Inventiones Mathematicae. 120:411-425

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::784cb53a458d97595ee7a6ef47bf4ddc
https://doi.org/10.1007/bf01241136

Twisted invariant theory for reflection groups

Autor: Gus Lehrer, Cédric Bonnafé, Jean Michel

Publikováno v: Nagoya Mathematical Journal
Nagoya Mathematical Journal, Duke University Press, 2006, 182, pp.135-170. ⟨10.1017/S0027763000026854⟩
Nagoya Mathematical Journal, 2006, 182, pp.135-170. ⟨10.1017/S0027763000026854⟩
Nagoya Math. J. 182 (2006), 135-170

Let $G$ be a reflection group acting on a vector space $V$ and let $\gamma$ be an automorphism of $V$ normalising $G$. We study how $\gamma$ acts on invariants and covariants (for various representations) of $G$, and properties of its eigenspaces.