On Schubert Varieties

Abstract

In this article we prove that a Schubert variety X(w) is a toric variety if and only if the Weyl group element w is a product of distinct simple reflections.

Key Words:

• Schubert variety
• Toric variety

2000 Mathematics Subject Classification:

• 14M15
• 14M25

ACKNOWLEDGMENT

The author would like to thank M. Brion for many discussions, especially on the proof of Lemma 3, and the anonymous referee for the remark.

Notes

Communicated by K. Misra.