Related papers: On Guay's evaluation map for affine Yangians

In this paper we formulate a conjecture which partially generalizes the Gross-Kohnen-Zagier theorem to higher weight modular forms. For f in S_k(N) satisfying certain conditions, we construct a map from the Heegner points of level N to a…

We construct certain integral structures for the cores of reduced tame extended affine Lie algebras of rank at least 2. One of the main tools to achieve this is a generalization of Chevalley automorphisms in the context of extended affine…

In 2016, Etingof defined the notion of a Yangian in a symmetric tensor category and posed the problem to study them in the context of Deligne categories. This problem was studied by Kalinov in 2020 for the Yangian $Y(\mathfrak{gl}_t)$ of…

We give a bijection between certain colored partitions and the elements in the quotient of an affine Weyl group modulo its Weyl group. By Bott's formula these colored partitions give rise to some partition identities. In certain types,…

In the previous paper, we constructed a homomorphism from the affine Yangian associated with $\widehat{\mathfrak{sl}}(n)$ to the standard degreewise completion of the affine Yangian associated with $\widehat{\mathfrak{sl}}(n+1)$. In this…

Let $U_q(\hat{\cal G})$ denote the quantized affine Lie algebra and $U_q({\cal G}^{(1)})$ the quantized {\em nontwisted} affine Lie algebra. Let ${\cal O}_{\rm fin}$ be the category defined in section 3. We show that when the deformation…

A general scheme of construction of Drinfeldians and Yangians from quantum non-twisted affine Kac-Moody algebras is presented. Explicit description of Drinfeldians and Yangians for all Lie algebras of the classical series A, B, C, D are…

We prove that an irreducible quasifinite module over the central extension of the Lie algebra of $N\times N$-matrix differential operators on the circle is either a highest or lowest weight module or else a module of the intermediate…

The existence of dual structures in a Yangian Y(g) signify that the latter belongs to multidimensional naturally parametrized variety of Hopf algebras. These varieties have boundaries containing Yangians Y(a) inequivalent to the original…

We construct a family of homomorphisms between Weyl modules for affine Lie algebras in characteristic p, which supports our conjecture on the strong linkage principle in this context. We also exhibit a large class of reducible Weyl modules…

A very useful result concerning flatness in Algebraic Geometry is EGA's ``fiber'' criterion. We propose similar fiber criteria to verify flatness of a module while avoiding ``finiteness'' assumptions. Motivated by a Tannakian viewpoint…

We define Weyl functors, global modules for equivariant map Lie superalgebras $(\g \otimes A)^{\Gamma}$, where $\g$ is basic classical $\mathbb{C}$- Lie superalgebra and $A$ is an associative commutative unital $\mathbb{C}$-algebra. Under…

We study the Yangians Y(a) associated with the simple Lie algebras a of type B, C or D. The algebra Y(a) can be regarded as a quotient of the extended Yangian X(a) whose defining relations are written in an R-matrix form. In this paper we…

In this paper we construct Young wall models for the level $1$ highest weight and Fock space crystals of quantum affine algebras in types $E_6^{(2)}$ and $F_4^{(1)}$. Our starting point in each case is a combinatorial realization for a…

The Seiberg-Witten map links noncommutative gauge theories to ordinary gauge theories, and allows to express the noncommutative variables in terms of the commutative ones. Its explicit form can be found order by order in the noncommutative…

We construct Wakimoto modules for twisted affine Lie algebras, and interpret the construction in terms of vertex algebras and their twisted modules. Using the Wakimoto realization, we prove the Kac-Kazhdan conjecture on the characters of…

We study a class of quantized enveloping algebras, called twisted Yangians, associated with the symmetric pairs of types B, C, D in Cartan's classification. These algebras can be regarded as coideal subalgebras of the extended Yangian for…

In general, quantum matrix algebras are associated with a couple of compatible braidings. A particular example of such an algebra is the so-called Reflection Equation algebra. In this paper we analyse its specific properties, which…

A new class of infinite dimensional representations of the Yangians $Y(\frak{g})$ and $Y(\frak{b})$ corresponding to a complex semisimple algebra $\frak{g}$ and its Borel subalgebra $\frak{b}\subset\frak{g}$ is constructed. It is based on…

This paper explores the irreducible uniformly bounded weight modules of map extended Special Lie algebras and map extended Hamiltonian Lie algebras under some condition on the action of the Laurent polynomial ring A_{N}.