Back to Commutative Algebra Seminar: Fall 2017
Commutative Algebra Seminar
Date: Friday, Oct 20, 2017
Time: 2:30PM - 3:20PM
Location: LCB 215
Alex Tchernev
SUNY, Albany
Title |
Determinantal hypersurfaces and representations of Coxeter groups |
Abstract |
Let ( A_1, …. , A_m ) be a tuple of n by n matrices with complex coefficients. We consider the hypersurface in complex affine m-space given by the equation det( - I + x_1 A_1 + … + x_m A_m ) = 0 where I is the identity matrix. Motivated by questions arising from functional analysis of operators on Hilbert spaces, we investigate how the geometry of this determinantal hypersurface reflects the mutual behavior of our matrices. The applications we will discuss in this talk are to the case when V is a complex n-dimensional unitary representation of a Coxeter group G with Coxeter generators g_1, … , g_m , and our matrices represent the action of the generators on V. This is joint work with Michael Stessin. |
Commutative Algebra