The prime spectrum of a quantum Bruhat cell translate

Abstract

The prime spectra of two families of algebras, $S^w$ and ${\check{S}}^w$, $w\in W,$ indexed by the Weyl group $W$ of a semisimple finitely dimensional are studied. The algebras $S^w$ have been introduced by A.~Joseph; they are $q$-analogues of the algebras of regular functions on $w$-translates of the open Bruhat cell of a semisimple Lie group $G$ corresponding to the Lie algebra $\fg$. We define a stratification of the spectra into components indexed by pairs $(y_1,y_2)$ of elements of the Weyl group satisfying $y_1\le w\le y_2$. 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.

AMS-LaTeX v1.2 (Compatibility mode), 35 pages

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