Related papers: Cell Systems for $\overline{\operatorname{Rep}(U_q…

In this article, we study the multiparameter second quantum Weyl algebra at roots of unity. In this setting, the algebra is a polynomial identity (PI) algebra, and the dimension of its simple modules is bounded above by its PI degree. We…

We present some observations on a restricted variant of unitary Cayley graphs modulo n, and the implications for a decomposition of elements of symplectic operators over the integers modulo n. We define quadratic unitary Cayley graphs G_n,…

We present several new examples of reflection principles which apply to both class groups of number fields and picard groups of of curves over $\mathbb{P}^{1}/\mathbb{F}_{p}$. This proves a conjecture of Lemmermeyer about equality of 2-rank…

Let $U_q(\mathfrak{g})$ be the quantum supergroup of $\mathfrak{gl}_{m|n}$ or the modified quantum supergroup of $osp_{m|2n}$ over the field of rational functions in $q$, and let $V_q$ be the natural module for $U_q(\mathfrak{g})$. There…

A conjecture of C. Bonnaf\'e, M. Geck, L. Iancu, and T. Lam parameterizes Kazhdan-Lusztig left cells for unequal parameter Hecke algebras in type $B_n$ by families of standard domino tableaux of arbitrary rank. Relying on a family of…

Let $\overline{\mathbb Q}$ be an algebraic closure of $\mathbb Q$ and let $A$ denote the ring of algebraic integers in $\overline{\mathbb Q}$. If $\mathcal S = \overline{\mathbb Q}^\times/A^\times$ then $\mathcal S$ is a vector space over…

We give a proof of Lusztig's conjectural multiplicity formula for non-restricted modules over the De Concini-Kac type quantized enveloping algebra at the $\ell$-th root of unity, where $\ell$ is an odd prime power satisfying certain…

Associated to any uniform finite layered graph Gamma there is a noncommutative graded quadratic algebra A(Gamma) given by a construction due to Gelfand, Retakh, Serconek and Wilson. It is natural to ask when these algebras are Koszul.…

We prove that the quantum graph algebra and the quantum moduli algebra associated to a punctured sphere and complex semisimple Lie algebra $\mathfrak{g}$ are Noetherian rings and finitely generated rings over $\mathbb{C}(q)$. Moreover, we…

In this paper, we study the Whittaker modules for the quantum enveloping algebra $U_q(\sl_3)$ with respect to a fixed Whittaker function. We construct the universal Whittaker module, find all its Whittaker vectors and investigate the…

Motivated by recent advances in the categorification of quantum groups at prime roots of unity, we develop a theory of 2-representations for 2-categories enriched with a p-differential which satisfy finiteness conditions analogous to those…

Let $G$ be a right-angled Artin group with defining graph $\Gamma$ and let $H$ be a finitely generated group quasi-isometric to $G(\Gamma)$. We show if $G$ satisfies (1) its outer automorphism group is finite; (2) $\Gamma$ does not have…

It is often stated that the Carlitz module is to the ring of univariate polynomials over a finite field what the multiplicative group is to the ring of integers. This analogy extends to the "rank 2" case, where Drinfeld modules play a role…

Let $F/{\mathbb Q}_p$ be a finite unramified extension, let $k$ be a finite extension of the residue field of $F$. We provide explicit constructions of integral structures for all rank two \'{e}tale Lubin-Tate $(\varphi,{\mathcal…

In this paper, we propose a novel graph kernel, namely the Quantum-based Entropic Subtree Kernel (QESK), for Graph Classification. To this end, we commence by computing the Average Mixing Matrix (AMM) of the Continuous-time Quantum Walk…

We study the semisimplicity of the category $KL_k$ for affine Lie superalgebras and provide a super analog of certain results from arXiv:1801.09880. Let $KL_k^{fin}$ be the subcategory of $KL_k$ consisting of ordinary modules on which the…

We study $p$-adic integral models of certain PEL Shimura varieties with level subgroup at $p$ related to the $\Gamma_1(p)$-level subgroup in the case of modular curves. We will consider two cases: the case of Shimura varieties associated…

We introduce a semisimple tensor category $\mc{O}^{int}_q(m|n)$ of modules over an quantum ortho-symplectic superalgebra. It is a natural counterpart of the category of finitely dominated integrable modules over the quantum classical…

Modular graph functions are $SL(2,{\mathbb Z})$-invariant functions associated with Feynman graphs of a two-dimensional conformal field theory on a torus of modulus $\tau$. For one-loop graphs they reduce to real analytic Eisenstein series.…

Knowledge graphs (KGs) play a crucial role in many applications, such as question answering, but incompleteness is an urgent issue for their broad application. Much research in knowledge graph completion (KGC) has been performed to resolve…