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Identities of Inverse Chevalley Type for the Graded Characters of Level-Zero Demazure Submodules over Quantum Affine Algebras of Type C
We provide identities of inverse Chevalley type for the graded characters of level-zero Demazure submodules of extremal weight modules over a quantum...
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On Minimal Tilting Complexes in Highest Weight Categories
We explain the construction of minimal tilting complexes for objects of highest weight categories and we study in detail the minimal tilting...
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On Modules M such that both M and M∗ are Semi-Gorenstein-Projective
Let A be an artin algebra. An A -module M is semi-Gorenstein-projective provided that Ext i ( M , A ) = 0 for all i ≥ 1. If M is Gorenstein-projective, then...
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Gluing Compact Matrix Quantum Groups
We study glued tensor and free products of compact matrix quantum groups with cyclic groups – so-called tensor and free complexifications. We...
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Non-Archimedean Duality: Algebras, Groups, and Multipliers
We develop a duality theory for multiplier Banach-Hopf algebras over a non-Archimedean field 𝕂. As examples, we consider algebras corresponding to...
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Pointed Hopf Algebras with Triangular Decomposition
In this paper, we present an approach to the definition of multiparameter quantum groups by studying Hopf algebras with triangular decomposition....
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Shilov Boundary for ”Holomorphic Functions” on a Quantum Matrix Ball
We describe the Shilov boundary ideal for a q-analog of the algebra of holomorphic functions on the unit ball in the space of 2×2 matrices
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Crystal energy functions via the charge in types A and C
The Ram–Yip formula for Macdonald polynomials (at t = 0) provides a statistic which we call charge. In types A and C it can be defined on tensor...
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Quantum duality principle for quantum Grassmannians
The quantum duality principle (QDP) for homogeneous spaces gives four recipes to obtain, from a quantum homogeneous space, a dual one, in the sense...
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F-Polynomials in Quantum Cluster Algebras
F -polynomials and g -vectors were defined by Fomin and Zelevinsky to give a formula which expresses cluster variables in a cluster algebra in terms of...
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Finite-Dimensional Representations of Hyper Loop Algebras over Non-algebraically Closed Fields
We study finite-dimensional representations of hyper loop algebras over non-algebraically closed fields. The main results concern the classification...
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Module Categories Over Representations of SL q (2) in the Non-Semisimple Case
We classify semisimple module categories over the tensor category of representations of quantum SL (2).
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History and Perspectives of Quantum Groups
The advent of Quantum Groups in the course of the working out the quantum analogue of the Inverse Scattering Method from the soliton theory gives an...
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A categorification of finite-dimensional irreducible representations of quantum \({\mathfrak{sl}_2}\) and their tensor products
The purpose of this paper is to study categorifications of tensor products of finite-dimensional modules for the quantum group for
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Cluster χ-varieties, amalgamation, and Poisson—Lie groups
In this paper, starting from a split semisimple real Lie group G with trivial center, we define a family of varieties with additional structures. We...