Related papers: Vogan classes in type $B_n$

This paper provides a serious attempt towards constructing a switching-algebraic theory for weighted monotone voting systems, whether they are scalar-weighted or vector-weighted. The paper concentrates on the computation of a prominent…

We define the notion of braided Coxeter category, which is informally a tensor category carrying compatible, commuting actions of a generalised braid group B_W and Artin's braid groups B_n on the tensor powers of its objects. The data which…

We incorporate a category of certain modules for an affine Lie algebra, of a certain fixed non-positive-integral level, considered by Kazhdan and Lusztig, into the representation theory of vertex operator algebras, by using the logarithmic…

With the aim of completing the previous study by A. Or{\l}owski and the author concerning intertwining maps between induced representations and conjugation representation, termed here weighted class operators, we compute the latter…

We give an analog of a Chevalley-Serre presentation for the Lie superalgebras W(n) and S(n) of Cartan type. These are part of a wider class of Lie superalgebras, the so-called tensor hierarchy algebras, denoted W(g) and S(g), where g…

Recently, Wang and the second author constructed a bar involution and canonical basis for a quasi-permutation module of the Hecke algebra associated to a type B Weyl group $W$, where the basis is parameterized by left cosets of a…

Kazhdan and Lusztig introduced the $W$-graphs, which represent the multiplication action of the standard basis on the canonical bais in the Iwahori-Hecke algebra. In the Hecke algebra module, Marberg defined two generalied $W$-graphs,…

For the BGG category of $\mathfrak{q}(n)$-modules of half-integer weights, a Kazhdan-Lusztig conjecture \`a la Brundan is formulated in terms of categorical canonical basis of the $n$th tensor power of the natural representation of the…

We develop a relative version of Kostant's harmonic theory and use this to prove a relative version of Kostant's theorem on Lie algebra (co)homology. These are associated to two nested parabolic subalgebras in a semisimple Lie algebra. We…

In this article, we discuss the notion of partition of elements in an arbitrary Coxeter system $(W,S)$: a partition of an element $w$ is a subset $\mathcal P\subseteq W$ such that the left inversion set of $w$ is the disjoint union of the…

In this paper, we examine the class of cofibrant modules over a group algebra $kG$, that were defined by Benson in [2]. We show that this class is always the left-hand side of a complete hereditary cotorsion pair in the category of…

We establish an isomorphism between certain complex-valued and vector-valued modular form spaces of half-integral weight, generalizing the well-known isomorphism between modular forms for $\Gamma_0(4)$ with Kohnen's plus condition and…

Let $(W,S)$ be any Coxeter system and let $w \mapsto w^*$ be an involution of $W$ which preserves the set of simple generators $S$. Lusztig and Vogan have shown that the corresponding set of twisted involutions (i.e., elements $w \in W$…

We study weight modules of the Lie algebra $W_2$ of vector fields on ${\mathbb C}^2$. A classification of all simple weight modules of $W_2$ with a uniformly bounded set of weight multiplicities is provided. To achieve this classification…

We obtain the equivariant K-homology of the classifying space \underline{E}W for W a right-angled or, more generally, an even Coxeter group. The key result is a formula for the relative Bredon homology of \underline{E}W in terms of Coxeter…

The graded cellularity of Libedinsky Double Leaves, which form a basis for the endomorphism ring of the Bott_Samelson_Soergel bimodules, allows us to view the Kazhdan_Lusztig polynomials as graded decomposition numbers. Using this point of…

Let k be an algebraically closed field of characteristic p>0 and let G be a symplectic or general linear group over k. We consider induced modules for G under the assumption that p is bigger than the greatest hook length in the partitions…

The study of Hermitian forms on a real reductive group $G$ gives rise, in the unequal rank case, to a new class of Kazhdan-Lusztig-Vogan polynomials. These are associated with an outer automorphism $\delta$ of $G$, and are related to…

From the bicovariant first order differential calculus on inhomogeneous Hopf algebra ${\cal B}$ we construct the set of right-invariant Maurer-Cartan one-forms considered as a right-invariant basis of a bicovariant ${\cal B}$-bimodule over…

On overview of Coxeter groups $W$, their Iwahori-Hecke algebras $H$, Lusztig's asymptotic algebras $J$, cellular algebras in general and cellularity of $H$ in particular, as well as an introduction to Gyoja's $W$-graph algebra and the…