English

An elementary construction of monomial bases of modified quantum affine $\mathfrak{gl}_n$

Quantum Algebra 2018-02-05 v2 Representation Theory

Abstract

In 1990 Beilinson, Lusztig and MacPherson provided a geometric realization of modified quantum gln\mathfrak{gl}_n and its canonical basis. A key step of their work is a construction of a monomial basis. Recently, Du and Fu provided an algebraic construction of the canonical basis for modified quantum affine gln\mathfrak{gl}_n, which among other results used an earlier construction of monomial bases using Ringel-Hall algebra of the cyclic quiver. In this paper, we give an elementary algebraic construction of a monomial basis for affine Schur algebras and modified quantum affine gln\mathfrak{gl}_n.

Keywords

Cite

@article{arxiv.1506.07263,
  title  = {An elementary construction of monomial bases of modified quantum affine $\mathfrak{gl}_n$},
  author = {Chun-Ju Lai and Li Luo},
  journal= {arXiv preprint arXiv:1506.07263},
  year   = {2018}
}

Comments

14 pages. Accepted by the Journal of London Mathematical Society. The introduction is reworded, and the references are updated. Some proofs are removed and now referred to the proper literature