## 5 Citations

### Quantum symmetric pairs

- Mathematics
- 2021

This is a survey of some recent progress on quantum symmetric pairs and applications. The topics include quasi K-matrices, ıSchur duality, canonical bases, super Kazhdan-Lusztig theory, ıHall…

### Symmetric subgroup schemes, Frobenius splittings, and quantum symmetric pairs

- Mathematics
- 2022

Let Gk be a connected reductive algebraic group over an algebraically closed field k of characteristic 6= 2. Let Kk ⊂ Gk be a quasi-split symmetric subgroup of Gk with respect to an involution θk of…

### Serre–Lusztig Relations for ı Quantum Groups

- Materials Science
- 2021

: Let ( U , U ı ) be a quantum symmetric pair of Kac–Moody type. The ı quantum groups U ı and the universal ı quantum groups (cid:2) U ı can be viewed as a generalization of quantum groups and…

### Serre–Lusztig Relations for $$\imath $$Quantum Groups

- Mathematics
- 2020

Let $(\bf U, \bf U^\imath)$ be a quantum symmetric pair of Kac-Moody type. The $\imath$quantum groups $\bf U^\imath$ and the universal $\imath$quantum groups $\widetilde{\bf U}^\imath$ can be viewed…

### A Serre presentation for the $\imath$quantum covering groups

- Mathematics
- 2019

Let $(\mathbf{U}, \mathbf{U}^\imath)$ be a quasi-split quantum symmetric pair of Kac-Moody type. The $\imath$quantum group $\mathbf{U}^\imath$ admits a Serre presentation featuring the $\imath$-Serre…

## References

SHOWING 1-10 OF 16 REFERENCES

### Introduction to Quantum Groups

- Mathematics
- 1998

We give an elementary introduction to the theory of algebraic and topological quantum groups (in the spirit of S. L. Woronowicz). In particular, we recall the basic facts from Hopf (*-) algebra…

### The bar involution for quantum symmetric pairs

- Mathematics
- 2014

We construct a bar involution for quantum symmetric pair coideal subalgebras $B_{\mathbf{c},\mathbf{s}}$ corresponding to involutive automorphisms of the second kind of symmetrizable Kac-Moody…

### A New Approach to Kazhdan-lusztig Theory of Type $b$ Via Quantum Symmetric Pairs

- Mathematics
- 2018

We show that Hecke algebra of type B and a coideal subalgebra of the type A quantum group satisfy a double centralizer property, generalizing the Schur-Jimbo duality in type A. The quantum group of…

### Finite-dimensional Hopf algebras arising from quantized universal enveloping algebra

- Mathematics
- 1990

0.1. An important role in the theory of modular representations is played by certain finite dimensional Hopf algebras u over Fp (the field with p elements, p = prime). Originally, u was defined…

### Symmetric Pairs for Quantized Enveloping Algebras

- Mathematics
- 1999

Abstract Let θ be an involution of a semisimple Lie algebra g , let g θ denote the fixed Lie subalgebra, and assume the Cartan subalgebra of g has been chosen in a suitable way. We construct a…

### Quantum groups at roots of ±1

- Mathematics
- 1996

Apart from being of interest in its own right, the representation theory for quantum groups at roots of unity enters into Lusztig’s programme (see e.g. [Lus94]) for determining the irreducible…

### Canonical bases arising from quantum symmetric pairs of Kac–Moody type

- MathematicsCompositio Mathematica
- 2021

For quantum symmetric pairs $(\textbf {U}, \textbf {U}^\imath )$ of Kac–Moody type, we construct $\imath$-canonical bases for the highest weight integrable $\textbf U$-modules and their tensor…

### Quantum groups at roots of 1

- Mathematics
- 1990

We extend to the not necessarily simply laced case the study [8] of quantum groups whose parameter is a root of 1.