We give a criterion for smoothness of a point in any Schubert variety in any
G/B in terms of the nil Hecke ring.Comment: AMSTE

A. Joseph

A. Ramanathan

B. Kostant

B.D. Boe

D. Kazhdan

D. Mumford

E. Cline

H.H. Andersen

I.N. Bernstein

J. Harris

J.B. Carrell

J.C. Jantzen

J.S. Wolper

K.M. Ryan

M.J. Dyer

N. Bourbaki

O. Mathieu

P. Polo

P. Slodowy

R. Hartshorne

S. Kumar

Shrawan Kumar

V. Lakshmibai

V.V. Deodhar

W. Rossmann

English

arXiv

Let G be a semi-simple simply-connected complex algebraic group and T ⊂ B a maximal torus and a Borel subgroup respectively. Let h = Lie T be the Cartan subalgebra of the Lie algebra Lie G, and W := N(T)/T the Weyl group associated to the pair (G, T), where N(T) is the normalizer of T in G. We can view any element w = w mod T ∈ W as the element (denoted by the corresponding German character) w of G/B, defined as w = wB. For any w ∈ W, there is associated the Schubert variety Xw := BwB/B ⊂ G/B and the T−fixed points of Xw (under the canonical left action) are precisely Iw := {v : v ∈ W and v ≤ w}

Kumar, Shrawan

Carolina Digital Repository

The nil Hecke ring and singularity of Schubert varieties

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http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.12.1227

The nil Hecke ring and singularity of Schubert varieties

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