Zobrazeno 1 - 10
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pro vyhledávání: '"Lehrer, G"'
Autor:
Lehrer, G. I., Zhang, R. B.
We introduce a diagram category, study its structure, and investigate some of its applications to the representation theory of Lie algebras and Lie superalgebras. The morphisms of the category, which contains a subcategory isomorphic to the Brauer ca
Externí odkaz:
http://arxiv.org/abs/2304.10174
Autor:
Lehrer, G. I., Zhang, R. B.
We introduce the notion of a diagram category and discuss its application to the invariant theory of classical groups and super groups, with some indications concerning extensions to quantum groups and quantum super groups. Tensor functors from vario
Externí odkaz:
http://arxiv.org/abs/2211.03924
Autor:
Lehrer, G. I.
We prove the following theorem. Let $G$ be a finite group generated by unitary reflections in a complex Hermitian space $V=\mathbb{C}^\ell$ and let $G'$ be any reflection subgroup of $G$. Let $\mathcal{H}(G)$ be the space of $G$-harmonic polynomials
Externí odkaz:
http://arxiv.org/abs/1812.03606
Autor:
Dyer, M. J., Lehrer, G. I.
Oshima's Lemma describes the orbits of parabolic subgroups of irreducible finite Weyl groups on crystallographic root systems. This note generalises that result to all root systems of finite Coxeter groups, and provides a self contained proof, indepe
Externí odkaz:
http://arxiv.org/abs/1708.00913
Autor:
Dyer, M. J., Lehrer, G. I.
We determine a fundamental domain for the diagonal action of a finite Coxeter group $W$ on $V^{\oplus n}$, where $V$ is the reflection representation. This is used to give a stratification of $V^{\oplus n}$, which is respected by the group action, an
Externí odkaz:
http://arxiv.org/abs/1707.03137
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:
http://arxiv.org/abs/1707.01196
When the parameter $q$ is a root of unity, the Temperley-Lieb algebra $TL_n(q)$ is non-semisimple for almost all $n$. Jones showed that there is a canonical symmetric bilinear form on $TL_n(q)$, whose radical $R_n(q)$ is generated by a certain idempo
Externí odkaz:
http://arxiv.org/abs/1702.08128
Let $U_q(\mathfrak{g})$ be the quantum supergroup of $\mathfrak{gl}_{m|n}$ or the modified quantum supergroup of $osp_{m|2n}$ over the field of rational functions in $q$, and let $V_q$ be the natural module for $U_q(\mathfrak{g})$. There exists a uni
Externí odkaz:
http://arxiv.org/abs/1602.04885
We give a new proof, inspired by an argument of Atiyah, Bott and Patodi, of the first fundamental theorem of invariant theory for the orthosymplectic super group. We treat in a similar way the case of the periplectic super group. Lastly, the same met
Externí odkaz:
http://arxiv.org/abs/1508.04202
Autor:
Lehrer, G. I., Zhang, R. B.
Given a complex orthosymplectic superspace $V$, the orthosymplectic Lie superalgebra $\mathfrak {osp}(V)$ and general linear algebra ${\mathfrak {gl}}_N$ both act naturally on the coordinate super-ring $\mathcal{S}(N)$ of the dual space of $V\otimes{
Externí odkaz:
http://arxiv.org/abs/1507.01329