Related papers: Almost dominant generalized slices and convolution…

We consider the Iwahori-Hecke algebra associated to an almost split Kac-Moody group $G$ (affine or not) over a nonarchimedean local field $K$. It has a canonical double-coset basis $(T_{\mathbf w})_{\mathbf w\in W^+}$ indexed by a…

(1) Suppose $\mu$ is a smooth measure on a hypersurface of positive Gaussian curvature in $\R^{2n}$. If $n\ge 2$, then $W(\mu)$, the Weyl transform of $\mu$, is a compact operator, and if $p>n\ge 6$ then $W(\mu)$ belongs to the $p$-Schatten…

Let $\pi : Z \to X$ be Galois cover of smooth projective curves with Galois group $W$ a Weyl group of a simple Lie group $G$. For a dominant weight $\lambda$, we consider the intermediate curve $Y_\lambda= Z/\Stab(\lambda)$. One can realise…

This paper is a brief review of recent results on the concept of ``generalized $\tau$-function'', defined as a generating function of all the matrix elements in a given highest-weight representation of a universal enveloping algebra ${\cal…

Many connections and dualities in representation theory can be explained using quasi-hereditary covers in the sense of Rouquier. The concepts of relative dominant and codominant dimension with respect to a module, introduced recently by the…

This paper introduces and systematically studies a new class of non-commutative algebras -- Weyl-type and Witt-type algebras -- generated by differential operators with exponential and generalized power function coefficients. We define the…

String diagrams turn algebraic equations into topological moves that have recurring shapes, involving the sliding of one diagram past another. We individuate, at the root of this fact, the dual nature of polygraphs as presentations of…

Given the symmetric group $G = \operatorname{Sym}(n)$ and a multiplicity-free subgroup $H\leq G$, the orbitals of the action of $G$ on $G/H$ by left multiplication induce a commutative association scheme. The irreducible constituents of the…

W.~Magnus' representations of submonoids $ E \leq \mbox{End}(F) $ of the endomorphisms of a free group $ F $ of finite rank are generalised by identifying them with the first homology group of $ F $ with particular coefficient modules. By…

Let $G$ be a connected semisimple algebraic group over an algebraically closed field of characteristic zero, and let $\th$ be an automorphism of $G$. We give a characterization of $\th$-twisted spherical conjugacy classes in $G$ by a…

We define a class of transversal slices in spaces which are quasi-Poisson for the action of a complex semisimple group G. This is a multiplicative analogue of Whittaker reduction. One example is the multiplicative universal centralizer of…

Let $\mathcal{G}$ be a split reductive $p$-adic group with connected centre. We show that each Bernstein block in the principal series of $\mathcal{G}$ admits a definite geometric structure, namely that of an extended quotient. For the…

We introduce a new construction, the isotropy groupoid, to organize the orbit data for split $\Gamma$-spaces. We show that equivariant principal $G$-bundles over split $\Gamma$-CW complexes $X$ can be effectively classified by means of…

Generalized splines are an algebraic combinatorial framework that generalizes and unifies various established concepts across different fields, most notably the classical notion of splines and the topological notion of GKM theory. The…

A generalized numerical semigroup is a submonoid $S$ of $\mathbb{N}^d$ with finite complement in it. We characterize isomorphisms between these monoids in terms of permutation of coordinates. Considering the equivalence relation that…

In this paper, we are interested in the decomposition of the tensor product of two representations of a symmetrizable Kac-Moody Lie algebra $\mathfrak g$. Let $P\_+$ be the set of dominant integral weights. For $\lambda\in P\_+$ ,…

We consider a class of quasi-Hopf algebras which we call \emph{generalized twisted quantum doubles}. They are abelian extensions $H = \mb{C}[\bar{G}] \bowtie \mb{C}[G]$ ($G$ is a finite group and $\bar{G}$ a homomorphic image), possibly…

We consider the Cartan subalgebra of any very extended algebra G+++ where G is a simple Lie algebra and let the parameters be space-time fields. These are identified with diagonal metrics and dilatons. Using the properties of the algebra,…

The ring of symmetric functions carries the structure of a Hopf algebra. When computing the coproduct of complete symmetric functions $h_\lambda$ one arrives at weighted sums over reverse plane partitions (RPP) involving binomial…

Let $G=GL_n(K)$ be the general linear group defined over an infinite field $K$ of positive characteristic $p$ and let $\Delta(\lambda)$ be the Weyl module of $G$ which corresponds to a partition $\lambda$. In this paper we classify all…