• Corpus ID: 236772311

$\imath$Schur Duality and Kazhdan-Lusztig basis expanded

@inproceedings{Shen2021imathSchurDA,
  title={\$\imath\$Schur Duality and Kazhdan-Lusztig basis expanded},
  author={Yaolong Shen and Weiqiang Wang},
  year={2021}
}
Expanding the classic work of Kazhdan-Lusztig and Deodhar, we establish bar involutions and canonical (i.e., quasi-parabolic KL) bases on quasi-permutation modules over the type B Hecke algebra, where the bases are parameterized by cosets of (possibly non-parabolic) reflection subgroups of the Weyl group of type B. We formulate an ıSchur duality between an ıquantum group of type AIII (allowing black nodes in its Satake diagram) and a Hecke algebra of type B acting on a tensor space, providing a… 
Generalized Schur-Weyl dualities for quantum affine symmetric pairs and orientifold KLR algebras
. We define a boundary analogue of the Kang-Kashiwara-Kim-Oh generalized Schur-Weyl dualities between quantum affine algebras and Khovanov-Lauda-Rouquier (KLR) algebras. Let g be a complex simple Lie

References

SHOWING 1-10 OF 40 REFERENCES
Kazhdan-Lusztig polynomials and canonical basis
AbstractIn this paper we show that the Kazhdan-Lusztig polynomials (and, more generally, parabolic KL polynomials) for the groupSn coincide with the coefficients of the canonical basis innth tensor
A New Approach to Kazhdan-lusztig Theory of Type $b$ Via Quantum Symmetric Pairs
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
THE q-SCHUR ALGEBRA
We study a class of endomomorphism algebras of certain q-permutation modules over the Hecke algebra of type B, whose summands involve both parabolic and quasi-parabolic subgroups, and prove that
Kazhdan-Lusztig Theory of super type D and quantum symmetric pairs
We reformulate the Kazhdan-Lusztig theory for the BGG category $\mathcal{O}$ of Lie algebras of type D via the theory of canonical bases arising from quantum symmetric pairs initiated by Weiqiang
Schur Algebras and Quantum Symmetric Pairs With Unequal Parameters
We study the (quantum) Schur algebras of type B/C corresponding to the Hecke algebras with unequal parameters. We prove that the Schur algebras afford a stabilization construction in the sense of
An Inversion Formula for -Relative Kazhdan–Lusztig Polynomials
The article proves a relative version of one of the results from the influential article [4] of Kazhdan and Lusztig which introduced the Kazhdan–Lusztig polynomials. Given a Coxeter group W and a set
Geometric Schur Duality of Classical Type
This is a generalization of the classic work of Beilinson, Lusztig and MacPherson. In this paper (and an Appendix) we show that the quantum algebras obtained via a BLM-type stabilization procedure in
Representations of Coxeter groups and Hecke algebras
here l(w) is the length of w. In the case where Wis a Weyl group and q is specialized to a fixed prime power, | ~ can be interpreted as the algebra of intertwining operators of the space of functions
Multiparameter quantum Schur duality of type B
We establish a Schur type duality between a coideal subalgebra of the quantum group of type A and the Hecke algebra of type B with 2 parameters. We identify the $\imath$-canonical basis on the tensor
Coideal Subalgebras and Quantum Symmetric Pairs
Coideal subalgebras of the quantized enveloping algebra are surveyed, with selected proofs included. The first half of the paper studies generators, Harish-Chandra modules, and associated quantum
...
...