Zobrazeno 1 - 10
of 2 792
pro vyhledávání: '"17B10"'
The celebrated Cauchy identity expresses the product of terms $(1 - x_i y_j)^{-1}$ for $(i,j)$ indexing entries of a rectangular $m\times n$-matrix as a sum over partitions $\lambda$ of products of Schur polynomials: $s_{\lambda}(x)s_{\lambda}(y)$. A
Externí odkaz:
http://arxiv.org/abs/2411.03117
Autor:
Kleshchev, Alexander
We explicitly compute the dimensions of certain idempotent truncations of RoCK blocks of cyclotomic quiver Hecke superalgebras. Equivalently, this amounts to a computation of the value of the Shapovalov form on certain explicit vectors in the basic r
Externí odkaz:
http://arxiv.org/abs/2411.02717
For a basic classical Lie superalgebra $\mathfrak s$, let $\mathfrak g$ be the central extension of the Takiff superalgebra $\mathfrak s\otimes\Lambda(\theta)$, where $\theta$ is an odd indeterminate. We study the category of $\mathfrak g$-Whittaker
Externí odkaz:
http://arxiv.org/abs/2410.22819
Autor:
Billig, Yuly, Rocha, Henrique
We study the growth of representations of the Lie algebra of vector fields on the affine space that admit a compatible action of the polynomial algebra. We establish the Bernstein inequality for these representations, enabling us to focus on modules
Externí odkaz:
http://arxiv.org/abs/2410.21121
Autor:
Cheng, Shun-Jen, Wang, Weiqiang
We establish a super duality as an equivalence between Whittaker module categories over a pair of classical Lie algebra and Lie superalgebra in the infinite-rank limit. Building on this result and utilizing the Losev-Shu-Xiao decomposition, we obtain
Externí odkaz:
http://arxiv.org/abs/2410.08617
In this paper we study realizations of highest weight modules for the complex Lie algebra $\mathfrak{gl}_n$ with respect to non-standard Gelfand-Tsetlin subalgebras. We also provide sufficient conditions for such subalgebras to have a diagonalizable
Externí odkaz:
http://arxiv.org/abs/2410.08011
Autor:
Gould, Mark, Zhang, Yang
In terms of highest weights, we establish branching rules for finite dimensional unitary simple modules of the general linear Lie superalgebra $\mathfrak{gl}_{m|n}$. Our proof uses the Howe duality for $\mathfrak{gl}_{m|n}$, as well as branching rule
Externí odkaz:
http://arxiv.org/abs/2410.04902
We introduce the notion of quasi-triangular Leibniz bialgebras, which can be constructed from solutions of the classical Leibniz Yang-Baxter equation (CLYBE) whose skew-symmetric parts are invariant. In addition to triangular Leibniz bialgebras, quas
Externí odkaz:
http://arxiv.org/abs/2410.03089
In an earlier publication, the last two authors showed that a finite-dimensional module for a quantum affine algebra of type $A$ whose $q$-factorization graph is totally ordered is prime. In this paper, we continue the investigation of the role of to
Externí odkaz:
http://arxiv.org/abs/2410.01519
New classes of Lie-Hamilton systems are obtained from the six-dimensional fundamental representation of the symplectic Lie algebra $\mathfrak{sp}(6,\mathbb{R})$. The ansatz is based on a recently proposed procedure for constructing higher-dimensional
Externí odkaz:
http://arxiv.org/abs/2409.18489