
Jie Xiao
Tsinghua University
Affine canonical bases and representations of tame quivers
Friday 10th October, 12:0512:55pm,
Carslaw 373.
According to a theorem of Green and Ringel, the generic
composition subalgebra of the Hall algebra provides a realization of the
positive part of quantum group. By using the explicit structure of the
category of representations of a tame quiver, we are able to construct a
PBWbasis of the generic composition algebra with a geometric order.
The matrix between this PBWbasis and a monomial basis is triangular with
1 on diagonal, then the canonical basis can be constructed by a linear
algebra technique ( from Lusztig too ). The material provided in the talk
is based on a joint work of Z.Lin, G.Zhang and J.Xiao.







