## 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