Zobrazeno 1 - 10
of 87
pro vyhledávání: '"17B10, 17B37"'
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
The concept of pseudo q-factorization graphs was recently introduced by the last two authors as a combinatorial language which is suited for capturing certain properties of Drinfeld polynomials. Using certain known representation theoretic facts abou
Externí odkaz:
http://arxiv.org/abs/2406.06970
Publikováno v:
Proc. Lond. Math. Soc. (3) 129 (2024), no. 3, Paper No. e12630
We introduce a family of cluster algebras of infinite rank associated with root systems of type $A$, $D$, $E$. We show that suitable completions of these cluster algebras are isomorphic to the Grothendieck rings of the categories $\mathcal{O}_\mathbb
Externí odkaz:
http://arxiv.org/abs/2401.04616
Autor:
Watanabe, Hideya
We provide a new branching rule from the general linear group $GL_{2n}(\mathbb{C})$ to the symplectic group $Sp_{2n}(\mathbb{C})$ by establishing a simple algorithm which gives rise to a bijection from the set of semistandard tableaux of a fixed shap
Externí odkaz:
http://arxiv.org/abs/2308.01718
Autor:
Mudrov, Andrey, Stukopin, Vladimir
Let $\mathcal{A}$ be an associative algebra containing either classical or quantum universal enveloping algebra of a semi-simple complex Lie algebra $\mathfrak{g}$. We present a construction of the Mickelsson algebra $Z(\mathcal{A},\mathfrak{g})$ rel
Externí odkaz:
http://arxiv.org/abs/2306.01592
We establish a version of Howe duality that involves a tensor product of Verma modules. Surprisingly, this duality leaves the realm of lowest and highest weight modules. We quantize this duality, and as an application, we prove that the (colored high
Externí odkaz:
http://arxiv.org/abs/2207.09124
Autor:
Stroppel, Catharina
Based on different views on the Jones polynomial we review representation theoretic categorified link and tangle invariants. We unify them in a common combinatorial framework and connect them via the theory of Soergel bimodules. The influence of thes
Externí odkaz:
http://arxiv.org/abs/2207.05139
Autor:
Moura, Adriano, Silva, Clayton
Publikováno v:
Comm in Algebra, 51, 4054-4090, 2023
We continue the study of prime simple modules for quantum affine algebras from the perspective of $q$-fatorization graphs. In this paper we establish several properties related to simple modules whose $q$-factorization graphs are afforded by trees. T
Externí odkaz:
http://arxiv.org/abs/2204.10442
Autor:
Moura, Adriano, Silva, Clayton
Publikováno v:
Canad. J. Math., 76 (2024), 594-637
We introduce the combinatorial notion of a $q$-fatorization graph intended as a tool to study and express results related to the classification of prime simple modules for quantum affine algebras. These are directed graphs equipped with three decorat
Externí odkaz:
http://arxiv.org/abs/2204.10439
Autor:
Mudrov, Andrey
Let $\mathfrak{g}$ be a simple complex Lie algebra of a classical type and $U_q(\mathfrak{g})$ the corresponding Drinfeld-Jimbo quantum group at $q$ not a root of unity. With every point $t$ of the fixed maximal torus $T$ of an algebraic group $G$ wi
Externí odkaz:
http://arxiv.org/abs/2201.04568