Related papers: Extended graphical calculus for categorified quant…
This paper introduces the category of marked curved Lie algebras with curved morphisms, equipping it with a closed model category structure. This model structure is---when working over an algebraically closed field of characteristic…
We prove a Burgess-like subconvex bound for twisted L-functions of a fixed irreducible cuspidal automorphic representation of GL(2) over a totally real number field. The proof is based on a spectral decomposition of shifted convolution sums…
Brundan and Kleshchev introduced graded decomposition numbers for representations of cyclotomic Hecke algebras of type $A$, which include group algebras of symmetric groups. Graded decomposition numbers are certain Laurent polynomials,…
We categorify the idempotented form of quantum sl(n).
We introduce a symmetric operad $\square p$ ("box-op") which describes a certain calculus of rectangular labeled ``boxes''. Algebras over $\square p$, which we call box operads, have appeared under the name of fc multicategories in work by…
In this paper, we study the structures of Schur algebra and Lusztig algebra associated to partial flag varieties of affine type D. We show that there is a subalgebra of Lusztig algebra and the quantum groups arising from this subalgebras…
The complexes of integral forms on the quantum Euclidean group $E_q(2)$ and the quantum plane are defined and their isomorphisms with the corresponding de Rham complexes are established.
The present paper continues the work of [10] and [6]. For any symmetrizable generalized Cartan Matrix $C$ and the corresponding quantum group $\mathbf{U}$, we consider the associated quiver $Q$ with an admissible automorphism $a$. We…
In this paper we construct all the primitive idempotents of the restricted quantum group $\overline{U}_q (sl_2)$ and also determine the multiplication rules among a basis given by the action of generators of $\bar{U}_q (sl_2)$ to the…
A simpler definition for a class of two-parameter quantum groups associated to semisimple Lie algebras is given in terms of Euler form. Their positive parts turn out to be 2-cocycle deformations of each other under some conditions. An…
In this paper we present explicit formulas for the *-product on quantum spaces which are of particular importance in physics, i.e., the q-deformed Minkowski space and the q-deformed Euclidean space in 3 and 4 dimensions, respectively. Our…
The two-parametric quantum superalgebra $U_{p,q}[gl(2/1)]$ is consistently defined. A construction procedure for induced representations of $U_{p,q}[gl(2/1)]$ is described and allows us to construct explicitly all (typical and nontypical)…
Let $\mathcal C$ be the category of finite graphs. Lov\`{a}sz shows that the semi-ring of isomorphism classes of $\mathcal C$ (with coproduct as sum, and product as multiplication) is embedded into the direct product of the semi-ring of…
This is a first part of a series of papers in which we develop explicit computational methods for automorphic forms for GL(3) and PGL(3) over elliptic function fields. In this first part, we determine explicit formulas for the action of the…
A Heisenberg-Clifford realization of a deformed $U(sl_{2})$ by two parameters $p$ and $q$ is discussed. The commutation relations for this deformed algebra have interesting connection with the theta functions.
Starting with the braided quantum group $\operatorname{SU}_q(2)$ for a complex deformation parameter $q$ we perform the construction of the quotient $\operatorname{SU}_q(2)/\mathbb{T}$ which serves as a model of a quantum sphere. Then we…
Abstract clones serve as an algebraic presentation of the syntax of a simple type theory. From the perspective of universal algebra, they define algebraic theories like those of groups, monoids and rings. This link allows one to study the…
We give an explicit isomorphism between the Gassner representation and the first weight level of a representation of quantum sl(2). Then we construct and provide matrices for colored versions of the BKL representation and higher Lawrence's…
We present a conceptual and uniform interpretation of the methods of integral representations of L-functions (period integrals, Rankin-Selberg integrals). This leads to: (i) a way to classify of such integrals, based on the classification…
Cusp forms are certain holomorphic functions defined on the upper half-plane, and the space of cusp forms for the principal congruence subgroup $\Gamma(p)$, $p$ a prime, is acted by $\mathrm{SL}_2(\mathbb{F}_p)$. Meanwhile, there is a…