Related papers: On Kostant's weight $q$-multiplicity formula for $…

We introduce general q-deformed multiple polylogarithms which even in the dilogarithm case differ slightly from the deformation usually discussed in the literature. The merit of the deformation as suggested, here, is that q-deformed…

The weight systems of finite-dimensional representations of complex, simple Lie algebras exhibit patterns beyond Weyl-group symmetry. These patterns occur because weight systems can be decomposed into lattice polytopes in a natural way.…

We give a new interpretation of representation theory of the finite-dimensional half-integer weight modules over the queer Lie superalgebra $\mathfrak{q}(n)$. It is given in terms of Brundan's work of finite-dimensional integer weight…

For every involution $\mathbf{w}$ of the symmetric group $S_n$ we establish, in terms ofa special canonical quotient of the dominant Verma module associated with $\mathbf{w}$, an effective criterion, which allows us to verify whether the…

For any Hermitian Lie group $G$ of tube type we give a geometric quantization procedure of certain $K_{\mathbb{C}}$-orbits in $\mathfrak{p}_{\mathbb{C}}^*$ to obtain all scalar type highest weight representations. Here $K_{\mathbb{C}}$ is…

We define global and local Weyl modules for $q \otimes A$, where $q$ is the queer Lie superalgebra and $A$ is an associative commutative unital $\mathbb{C}-$algebra. We prove that global Weyl modules are universal highest weight objects in…

The authors compute the support varieties of all irreducible modules for the small quantum group $u_\zeta(\mathfrak{g})$, where $\mathfrak{g}$ is a simple complex Lie algebra, and $\zeta$ is a primitive $\ell$-th root of unity with $\ell$…

Several kinds of q-orthogonal polynomials with |q|=1 are constructed as the main parts of the eigenfunctions of new solvable discrete quantum mechanical systems. Their orthogonality weight functions consist of quantum dilogarithm functions,…

We introduce a universal weight system (a function on chord diagrams satisfying the $4$-term relation) taking values in the ring of polynomials in infinitely many variables whose particular specializations are weight systems associated with…

We introduce the multiset partition algebra $\mathcal{MP}_k(\xi)$ over $F[\xi]$, where $F$ is a field of characteristic $0$ and $k$ is a positive integer. When $\xi$ is specialized to a positive integer $n$, we establish the Schur-Weyl…

We propose a closed formula of the universal part of supersymmetric R\'enyi entropy $S_q$ for $(2,0)$ superconformal theories in six-dimensions. We show that $S_q$ across a spherical entangling surface is a cubic polynomial of…

Following Lusztig, we consider a Coxeter group $W$ together with a weight function $L$. This gives rise to the pre-order relation $\leq_{L}$ and the corresponding partition of $W$ into left cells. We introduce an equivalence relation on…

Let $n$ and $t$ be positive integers with $t\geq 2$. Let $R_t(n)$ be the number of $t$-regular partitions of $n$. A class of functions, denoted $\tau_k(n)$, is defined as follows:…

Weighted model counting (WMC) has proven effective at a range of tasks within computer science, physics, and beyond. However, existing approaches for using WMC in quantum physics only target specific problem instances, lacking a general…

Weighted First-Order Model Counting (WFOMC) computes the weighted sum of the models of a first-order logic theory on a given finite domain. First-Order Logic theories that admit polynomial-time WFOMC w.r.t domain cardinality are called…

We provide a systematic approach to obtain formulas for characters and Kostant ${\mathfrak u}$-homology groups of the oscillator modules of the finite dimensional general linear and ortho-symplectic superalgebras, via Howe dualities for…

We develop the theory of weighted P-partitions, which generalises the theory of P-partitions from labelled posets to weighted labelled posets. We define the related generating functions in the natural way and compute their product,…

We present a method of finding weighted Koppelman formulas for $(p,q)$-forms on $n$-dimensional complex manifolds $X$ which admit a vector bundle of rank $n$ over $X \times X$, such that the diagonal of $X \times X$ has a defining section.…

Let $G$ be a reductive group over a field of prime characteristic. An indecomposable tilting module for $G$ whose highest weight lies above the Steinberg weight has a character that is divisible by the Steinberg character. The resulting…

We study certain overlap coefficients appearing in representation theory of the quantum algebra $\U_q(\mathfrak{sl}_2(\C))$. The overlap coefficients can be identified as products of Askey-Wilson functions, leading to an algebraic…