The prime spectrum of a quantum analogue of the ring of regular functions on the open Bruhat cell translate

Abstract

The prime spectrum of a quantum analogue R o w of the ring of regular functions on the w-translate of the open Bruhat cell is studied in the spirit of [3]. We define a stratification of the spectrum into components indexed by pairs ( y 1, y 2) of elements of the Weyl group satisfying y 1 ≤ w ≤ y 2. Each component admits a unique minimal ideal which is explicitly described. We show the inclusion relation of closures to be that induced by Bruhat order.