Related papers: Note on Exponents Associated with Y-Systems

Let W be the Weyl group of a crystallographic root system acting on the associated weight lattice by reflections. In the present notes we extend the notion of an exponent of the W-action introduced in [Baek-Neher-Zainoulline,…

We introduce a signed variant of (valued) quivers and a mutation rule that generalizes the classical Fomin-Zelevinsky mutation of quivers. To any signed valued quiver we associate a matrix that is a signed analogue of the Cartan counterpart…

The aim of this paper is two-fold: (1) introduce four systems of equations called M-systems and dual M-systems of types $A_{n}$ and $B_{n}$ respectively; (2) make a connection between M-systems (dual M-systems) and cluster algebras and…

For a finite subgroup $G$ of the special unitary group $SU_2$, we study the centralizer algebra $Z_k(G) = End_G(V^{\otimes k})$ of $G$ acting on the $k$-fold tensor product of its defining representation $V= \mathbb{C}^2$. These subgroups…

We conjecture that if a system S \subseteq {x_i=1, x_i+x_j=x_k, x_i \cdot x_j=x_k: i,j,k \in {1,...,n}} has only finitely many solutions in integers x_1,...,x_n, then each such solution (x_1,...,x_n) satisfies |x_1|,...,|x_n| \leq…

We present the evaluation of a family of exponential-logarithmic integrals. These have integrands of the form P(exp(x),ln(x)) where P is a polynomial. The examples presented here appear in sections 4.33, 4.34 and 4.35 in the classical table…

The aim of this paper is twofold. The first one is to find several relations between the type 2 higher-order degenerate Euler polynomials and the type 2 higher-order Changhee polynomials in connection with the degenerate stirling numbers of…

Let $(X_{k})_{k\geq 1}$ and $(Y_k)_{k\geq 1}$ be the sequence of $X$ and $Y$-coordinates of the positive integer solutions $(x, y)$ of the equation $x^2 - dy^2 = t$. In this paper we completely describe those recurrence sequences such that…

In one of his papers, the author introduces the class of Farkas-related vectors for which a version of Farkas' lemma over integers is derived. In this paper, two similar classes are introduced and studied.

Let P be the set of the sequence of polynomials of degree n. The aim of this paper is to study the Stirling numbers of the second kind associated with P and of the first kind associated with P, in a unified and systematic way with the help…

In this paper we establish an order statistics model of Young tableaux. Multiple integration over nested simplexes is applied to the enumeration of Young tableaux. A brief proof of Frobenius-Young's and Aitken's formulas is given. Partially…

We develop an analog of the exponential families of Wilf in which the label sets are finite dimensional vector spaces over a finite field rather than finite sets of positive integers. The essential features of exponential families are…

This is a sequel to the second and third author's Mixed Dimer Configuration Model in Type $D$ Cluster Algebras where we extend our model to work for quivers that contain oriented cycles. Namely, we extend a combinatorial model for…

Let $Q$ be the Dynkin quiver of type $\mathbb{D}_{n}$ with linear orientation and let $Q'$ be the quiver formed by reversing the arrow at the unique source in $Q$. In this paper, we present a complete classification of both silted algebras…

There is a connection between *-representations of algebras associated with graphs and the problem about the spectrum of a sum of Hermitian operators (spectral problem). For algebras associated with extended Dynkin graphs we give an…

The zeros of classical Eisenstein series satisfy many intriguing properties. Work of F. Rankin and Swinnerton-Dyer pinpoints their location to a certain arc of the fundamental domain, and recent work by Nozaki explores their interlacing…

Correlators based on $s\ell_2$ Yangian symmetry and its quantum deformation are studied. Symmetric integral operators can be defined with such correlators as kernels. Yang-Baxter operators can be represented in this way. Particular Yangian…

We generalise Koszul and D-Koszul algebras by introducing a class of graded algebras called (D,A)-stacked algebras. We give a characterisation of (D,A)-stacked algebras and show that their Ext algebra is finitely generated as an algebra in…

We study the $SU(2)$ WZNW model over a family of elliptic curves. Starting from the formulation developed by Tsuchiya, Ueno and Yamada, we derive a system of differential equations which contains the Knizhnik-Zamolodchikov-Bernard…

Let $M$ be the Shimura variety associated to the group of spinor similitudes of a quadratic space over $\mathbb{Q}$ of signature $(n,2)$. We prove a conjecture of Bruinier and Yang, relating the arithmetic intersection multiplicities of…