MONOMIAL BASES FOR q-SCHUR ALGEBRAS

@inproceedings{Jie2002MONOMIALBF,
  title={MONOMIAL BASES FOR q-SCHUR ALGEBRAS},
  author={Du Jie and Brian J. Parshall},
  year={2002}
}
Using the Beilinson-Lusztig-MacPherson construction of the quantized enveloping algebra of gln and its associated monomial basis, we investigate q-Schur algebras Sq(n, r) as “little quantum groups”. We give a presentation for Sq(n, r) and obtain a new basis for the integral q-Schur algebra Sq(n, r), which consists of certain monomials in the original generators. Finally, when n > r, we interpret the Hecke algebra part of the monomial basis for Sq(n, r) in terms of Kazhdan-Lusztig basis elements… CONTINUE READING