Related papers: A weight multiplicity formula for Demazure modules

For $G$ a complex reductive group and $B \subseteq G$ a Borel subgroup, we provide a reduction rule for certain weight multiplicities in Demazure modules $V_\lambda^w$: given a weight $\mu$ on a face of the associated weight polytope…

A bivariate representation of a complex simple Lie algebra is an irreducible representation having highest weight a combination of the first two fundamental weights. For a complex classical Lie algebra, we establish an expression for the…

Let $\mathfrak{g}$ be a finite-dimensional complex simple Lie algebra with highest root $\theta$ and let $\mathfrak{g}[t]$ be the corresponding current algebra. In this paper, we consider the $\mathfrak{g}[t]$-stable Demazure modules…

We give a twining character formula for Demazure modules.

We develop a general framework for studying relative weight representations for certain pairs consisting of an associative algebra and a commutative subalgebra. Using these tools we describe projective and simple weight modules for quantum…

The multiplicity of a weight $\mu$ in an irreducible representation of a simple Lie algebra $\mathfrak{g}$ with highest weight $\lambda$ can be computed via the use of Kostant's weight multiplicity formula. This formula is an alternating…

We develop a theory of weights for a quantum analogue of the symmetric pair (gl4,gl2 x gl2) realised as a quantum symmetric pair subalgebra. Based on Letzter's triangular decomposition we define Verma modules. Using magical operators that…

Let $G$ be a compact semisimple Lie group and $T$ be a maximal torus of $G$. We describe a method for weight multiplicity computation in unitary irreducible representations of $G$, based on the theory of Berezin quantization on $G/T$. Let…

We obtain inductive and enumerative formulas for the multiplicities of the weights of the spin module for the Clifford algebra of a Levi subalgebra in a complex semisimple Lie algebra. Our formulas involve only matrices and tableaux, and…

We determine the covariance of the weight distribution in level 1 Demazure modules of sl2hat. This allows us to prove a weak law of large numbers for these weight distributions, and leads to a conjecture about the asymptotic concentration…

The purpose of this note is to define and construct highest weight modules for Felder's elliptic quantum groups. This is done by using exchange matrices for intertwining operators between (not necessarily finite-dimensional) modules over…

This paper is based on the observation that dimension of weight spaces of multi-variable Weyl modules depends polynomially on the highest weight (Conjecture 1). We support this conjecture by various explicit answers for up to three variable…

For $G$ a reductive group and $T\subset B$ a maximal torus and Borel subgroup, Demazure modules are certain $B$-submodules, indexed by elements of the Weyl group, of the finite irreducible representations of $G$. In order to describe the…

Let $\mathfrak{g}$ be a semisimple Lie algebra over $\mathbb{C}$ having rank $l$ and let $V=L(\lambda)$ be an irreducible finite-dimensional $\mathfrak{g}$-module having highest weight $\lambda.$ Computations of weight multiplicities in…

This paper establishes mixed multiplicity formulas concerning the relationship between mixed multiplicities of modules and mixed multiplicities of rings via rank of modules.

We compute the expected degree of a randomly chosen element in a basis of weight vectors in the Demazure module $V_w(\Lambda)$ of $\hat{sl}_2$. We obtain en passant a new proof of Sanderson's dimension formula for these Demazure modules.

We study Demazure modules which occur in a level $\ell$ irreducible integrable representation of an affine Lie algebra. We also assume that they are stable under the action of the standard maximal parabolic subalgebra of the affine Lie…

For any finite-dimensional simple Lie algebra $\mathfrak{g}$ and commutative associative algebra $S$ of finite type, we give a complete classification of the simple weight modules of $\mathfrak{g}\otimes S$ with bounded weight…

We define a weighted multiplicity function for closed geodesics of given length on a finite area Riemann surface. These weighted multiplicities appear naturally in the Selberg trace formula, and in particular their mean square plays an…

We express the multiplicities of the irreducible summands of certain tensor products of irreducible integrable modules for an affine Kac-Moody algebra over a simply laced Lie algebra as sums of multiplicities in appropriate excellent…