We will describe combinatorial "models" that can be used to study various quantum algebras (for example quantum matrices, quantum symmetric and skew-symmetric matrices, the quantum grassmannian and more). For all of these algebras, there is an action of an algebraic torus by automorphisms and a description of the torus-invariant prime ideals is a key step towards understanding the full prime spectrum due to work of Goodearl and Letzter. We will discuss how the above combinatorial models can be used to calculate Grobner bases of all torus-invariant prime ideals, as well as provide other useful information. Portions of this talk are joint work with Stephane Launois.
Combinatorial Models of Quantum Matrix Algebras
Karel Casteels (Kent)
Mon, 23/03/2015 - 16:30