8 Citations
A categorification of finite-dimensional irreducible representations of quantum $${\mathfrak{sl}_2}$$ and their tensor products
- Mathematics
- 2007
Abstract.The purpose of this paper is to study categorifications of tensor products of finite-dimensional modules for the quantum group for
$${\mathfrak{sl}_2}$$
. The main categorification is…
Yang–Baxter algebras, convolution algebras, and Grassmannians
- MathematicsRussian Mathematical Surveys
- 2020
This paper surveys a new actively developing direction in contemporary mathematics which connects quantum integrable models with the Schubert calculus for quiver varieties: there is a purely…
Yang-Baxter algebras as convolution algebras: The Grassmannian case
- Mathematics
- 2018
We present a simple but explicit example of a recent development which connects quantum integrable models with Schubert calculus: there is a purely geometric construction of solutions to the…
EXTENDED QUANTUM ENVELOPING ALGEBRAS OF sl(2)
- Mathematics
- 2009
In present paper we define a new kind of quantized enveloping algebra of sl(2). We denote this algebra by Ur,t, where r, t are two non-negative integers. It is a non-commutative and non-cocommutative…
EXTENDED QUANTUM ENVELOPING ALGEBRAS OF (2)
- MathematicsGlasgow Mathematical Journal
- 2009
Abstract In present paper we define a new kind of quantized enveloping algebra of (2). We denote this algebra by Ur,t, where r, t are two non-negative integers. It is a non-commutative and…
A categorification of finite-dimensional irreducible representations of quantum sl(2) and their tensor products
- Mathematics
- 2005
The purpose of this paper is to study categorifications of tensor products of finite dimensional modules for the quantum group for sl(2). The main categorification is obtained using certain…
References
SHOWING 1-10 OF 17 REFERENCES
Tensor product varieties and crystals. ADE case
- Mathematics
- 2001
Let g be a simple simply laced Lie algebra. In this paper two families of varieties associated to the Dynkin graph of g are described: ``tensor product'' and ``multiplicity'' varieties. These…
Quiver varieties and tensor products
- Mathematics
- 2001
Abstract.In this article, we give geometric constructions of tensor products in various categories using quiver varieties. More precisely, we introduce a lagrangian subvariety &?tilde; in a quiver…
Instantons on ALE spaces, quiver varieties, and Kac-Moody algebras
- Mathematics
- 1994
To Professor Shoshichi Kobayashi on his 60th birthday 1. Introduction. In this paper we shall introduce a new family of varieties, which we call quiver varieties, and study their geometric…
Canonical bases in tensor products.
- MathematicsProceedings of the National Academy of Sciences of the United States of America
- 1992
I construct a canonical basis in the tensor product of a simple integrable highest weight module with a simple integrable lowest weight module of a quantized enveloping algebra. This basis is…
Perverse sheaves and quantum Grothendieck rings
- Mathematics
- 2003
We give a geometric construction of a deformation of the Grothendieck ring of finite-dimensional representations of quantized affine algebras. It yields a positivity result for products of some…
Quantum Groups
- Mathematics
- 1994
Here is an introduction to the theory of quantum groups with emphasis on the spectacular connections with knot theory and Drinfeld's recent fundamental contributions. It presents the quantum groups…
An introduction to intersection homology theory.
- Mathematics
- 1988
INTRODUCTION Poincare duality Morse theory for siningular spac es de Rham cohomology and L2-c -cohomol ology The cohomology of pr projective vari ties REVIEW OF HOMOLOGY AND COHOMOLOGY Simplicial…
Canonical bases in tensor products and graphical calculus for Uqðsl2Þ; Duke Math
- J. 87 (3)
- 1997