Related papers: Stabilized plethysms for the classical Lie groups

Local Weyl modules over two-dimensional currents with values in $gl_r$ are deformed into spaces with bases related to parking functions. Using this construction we 1) propose a simple proof that dimension of the space of diagonal…

We introduce the new combinatorial approach of plethystic type of tableaux, as a method to understand coefficients of Schur functions appearing in plethysms $s_\nu[h_\lambda]$ and $s_{\nu}[e_{\lambda}]$, for any partitions $\lambda$ and…

By exploiting relationships between the values taken by ordinary characters of symmetric groups we prove two theorems in the modular representation theory of the symmetric group. 1. The decomposition matrices of symmetric groups in odd…

We characterize charmenability among arithmetic groups and deduce dichotomy statements pertaining normal subgroups, characters, dynamics, representations and associated operator algebras. We do this by studying the stationary dynamics on…

Using the Weyl commutation relations over a finite field we introduce a family of error-correcting quantum stabilizer codes based on a class of symmetric matrices over the finite field satisfying certain natural conditions. When the field…

We investigate structural and rigidity properties of \emph{Lie skew braces} (LSBs), objects essentially known in the literature as \emph{post--Lie groups}, obtained by endowing a manifold with two compatible group laws that share the same…

The Macdonald symmetric functions are used to define measures on the set of all partitions of all integers. Probabilistic algorithms are given for growing partitions according to these measures. The case of Hall-Littlewood polynomials is…

Let $\mathfrak{g}$ be a finite-dimensional simple complex Lie algebra. A layer sum is introduced as the sum of formal exponentials of the distinct weights appearing in an irreducible $\mathfrak{g}$-module. It is argued that the character of…

We study a spectral problem related to the finite-dimensional characters of the groups $Sp(2N)$, $SO(2N+1)$, and $SO(2N)$, which form the classical series $C$, $B$, and $D$, respectively. The irreducible characters of these three series are…

A correction factor naturally arises in the theory of p-adic Kac--Moody groups. In this paper, we expand the correction factor into a sum of irreducible characters of the underlying Kac--Moody algebra. We derive a formula for the…

This is the first of a series of papers devoted to certain pairs of commuting nilpotent elements in a semisimple Lie algebra that enjoy quite remarkable properties and which are expected to play a major role in Representation theory. The…

The standard stabilizer formalism provides a setting to show that quantum computation restricted to operations within the Clifford group are classically efficiently simulable: this is the content of the well-known Gottesman-Knill theorem.…

Partition functions arise in statistical physics and probability theory as the normalizing constant of Gibbs measures and in combinatorics and graph theory as graph polynomials. For instance the partition functions of the hard-core model…

We provide a combinatorial description of the coefficients appearing in the expansion of Hall-Littlewood polynomials in terms of monomial symmetric functions. We also give a Littlewood-Richardson rule for Hall-Littlewood polynomials. For…

We generalize a theorem of Littlewood concerning the factorization of Schur polynomials when their variables are twisted by roots of unity. We show that a certain family of flagged skew Schur polynomials admit a similar factorization. These…

The coefficient algebra of a finite-dimensional Lie algebra on a finite-dimensional representation is defined as the subalgebra generated by all coefficients of the corresponding characteristic polynomial. We explore connections between…

Plethysm of two Schur functions can be expressed as a linear combination of Schur functions, and monomial symmetric functions. In this paper, we express the coefficients combinatorially in the case of monomial symmetric functions. And by…

We prove a homological stability theorem for families of discrete groups (e.g. mapping class groups, automorphism groups of free groups, braid groups) with coefficients in a sequence of irreducible algebraic representations of arithmetic…

We discuss the deformed function algebra of a simply connected reductive Lie group G over the complex numbers using a basis consisting of matrix elements of finite dimensional representations. This leads to a preferred deformation, meaning…

Let $U_q$ denote the quantum group associated with a finite dimensional semisimple Lie algebra. Assume that $q$ is a complex root of unity of odd order and that $U_q$ is %the quantum group version obtained via Lusztig's $q$-divided powers…