相关论文: Visualizing the Support of Kostant's Weight Multip…

Let $\mathfrak g$ be a complex semisimple Lie algebra. We obtain new properties of the $q$-analogue of weight multiplicities in finite-dimensional representations of $\mathfrak g$. In particular, it is proved that certain weighted sum of…

We describe a systematic method to construct arbitrary highest-weight modules, including arbitrary finite-dimensional representations, for any finite dimensional simple Lie algebra $\mathfrak{g}$. The Lie algebra generators are represented…

We present a closed form for a multi-variate generating function for the dimensions of the irreducible representations of a semisimple, simply connected linear algebraic group over $\mathbb{C}$ whose highest weights lie in a finitely…

Dominant weight multiplicities of simple Lie groups are expressed in terms of the modular matrices of Wess-Zumino-Witten conformal field theories, and related objects. Symmetries of the modular matrices give rise to new relations among…

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…

In physics, Lie groups represent the algebraic structure that describes symmetry transformations of a given system. Then, the descending Lie algebra of those groups are necessarily real. In most cases, the complexification of those Lie…

We determine the multiplicity of the irreducible representation V(n) of the simple Lie algebra sl(2,C) as a direct summand of its fourth exterior power $\Lambda^4 V(n)$. The multiplicity is 1 (resp. 2) if and only if n = 4, 6 (resp. n = 8,…

We present `liesuperalg` a SageMath package for representation-theoretic calculations involving Lie superalgebras in Type A. Our package introduces functionality to calculate invariants of weights and produce the associated cup diagrams. We…

We study weight posets of weight multiplicity free (=wmf) representations $R$ of reductive Lie algebras. Specifically, we are interested in relations between $\dim R$ and the number of edges in the Hasse diagram of the corresponding weight…

We study the category $\cal I_{\gr}$ of graded representations with finite--dimensional graded pieces for the current algebra $\lie g\otimes\bc[t]$ where $\lie g$ is a simple Lie algebra. This category has many similarities with the…

We investigate the category of finite-dimensional representations of twisted hyper loop algebras, i.e., the hyperalgebras associated to twisted loop algebras over finite-dimensional simple Lie algebras. The main results are the…

Let g be a semisimple Lie algebra over the real numbers. We describe an explicit combinatorial construction of the real Weyl group of g with respect to a given Cartan subalgebra. An efficient computation of this Weyl group is important for…

Given a hyper loop algebra over a non-algebraically closed field, we address multiplicity problems in the underlying abelian tensor category of finite-dimensional representations. Namely, we give formulas for the l-characters of the simple…

We study finite-dimensional representations of hyper loop algebras, i.e., the hyperalgebras over an algebraically closed field of positive characteristic associated to the loop algebra over a complex finite-dimensional simple Lie algebra.…

This review paper contains a concise introduction to highest weight representations of infinite dimensional Lie algebras, vertex operator algebras and Hilbert schemes of points, together with their physical applications to elliptic genera…

It is known that summations over Weyl groups of Lie algebras is a problem which enters in many areas of physics as well as in mathematics. For this, a method which we would like to call {\bf permutation weights} has been previously proposed…

We classify simple weight modules over infinite dimensional Weyl algebras and realize them using the action on certain localizations of the polynomial ring. We describe indecomposable projective and injective weight modules and deduce from…

We give a complete combinatorial answer to Kostant's problem for simple highest weight modules indexed by fully commutative permutations. We also propose a reformulation of Kostant's problem in the context of fiab bicategories and classify…

The weights of finite-dimensional representations of simple Lie algebras are naturally associated with Weyl polytopes. Representation characters decompose into multiplicity-free sums over the weights in Weyl polytopes. The Brion formula for…

This paper establishes a novel combinatorial framework at the intersection of Lie theory and algebraic combinatorics, based on a generalization of the Kostant game. We begin by reviewing the foundations of root systems, the classification…