
Jie Du
University of New South Wales
Infinitesimal quantum gl_{n} and little qSchur algebras
Friday 11th June, 12:0512:55pm,
Carslaw 373.
We first follow De Concini and Kac
to give a presentation for the infinitesimal quantum
gl_{n}, u_{k}(n), and then reconstruct or
realize u_{k}(n)
in two different ways following the BeilinsonLusztigMacPherson
geometric setting approach. Thus, we obtain three new
bases for u_{k}(n). Then, we use
u_{k}(n) to introduce the little qSchur algebra u_{k}(n,r)
as a subalgebra of the qSchur algebra U_{k}(n,r). The symmetry
structure of a little qSchur algebra is then investigated
through the construction of various bases of monomial, BLM and PBW
types for u_{k}(n) and qSchur algebras. We also obtain a
formula for the dimension of u_{k}(n,r).







