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Singular Loci of Schubert Varieties

- S. Billey, V. Lakshmibai
- Mathematics
- 29 September 2000

This text presents topics in a systematic fashion to engage a wide readership. It includes: generalities on G/B and G/Q; the Grassmannian and the flag variety SL_n/B' the tangent space and… Expand

Criterion for smoothness of Schubert varieties in Sl(n)/B

- V. Lakshmibai, B. Sandhya
- Mathematics
- 1 April 1990

LetG=Sl(n) andB, the Borel subgroup ofG consisting of upper triangular matrices. Letw∈Sn andX(w)=BwB(modB), the associated Schubert variety inG/B. In this paper, we give a geometric criterion for the… Expand

Degenerations of flag and Schubert varieties to toric varieties

- N. Gonciulea, V. Lakshmibai
- Mathematics
- 1 September 1996

In this paper, we prove the degenerations of Schubert varieties in a minusculeG/P, as well as the class of Kempf varieties in the flag varietySL(n)/B, to (normal) toric varieties. As a consequence,… Expand

Geometry of GP−V

- V. Lakshmibai, C. S. Seshadri
- Mathematics
- 1 May 1986

We summarise here the main results of Geometry ofG/P-I, . . , IV(cf. 17] > [6] > [4], [5]). The purpose is to extend the Hodge-Young standard monomial theory for the group SL(ri) (cf. [2] ) to the… Expand

Standard Monomial Theory for Bott–Samelson Varieties

- V. Lakshmibai, P. Littelmann, P. Magyar
- Mathematics
- Compositio Mathematica
- 1 February 2002

Bott–Samelson varieties are an important tool in geometric representation theory [1, 3, 10, 25]. They were originally defined as desingularizations of Schubert varieties and share many of the… Expand

Equivariant Giambelli and determinantal restriction formulas for the Grassmannian

- V. Lakshmibai, K. Raghavan, P. Sankaran
- Mathematics
- 1 June 2005

The main result of the paper is a determinantal formula for the restriction to a torus fixed point of the equivariant class of a Schubert subva- riety in the torus equivariant integral cohomology… Expand

Frobenius Splittings and Blow-ups

- V. Lakshmibai, V. Mehta, A. J. Parameswaran
- Mathematics
- 1 October 1998

Standard Monomial Theory: Invariant Theoretic Approach

- V. Lakshmibai, K. Raghavan
- Mathematics
- 23 December 2007

Generalities on algebraic varieties.- Generalities on algebraic groups.- Grassmannian.- Determinantal varieties.- Symplectic Grassmannian.- Orthogonal Grassmannian.- The standard monomial theoretic… Expand

Standard Monomial Theory and applications

- V. Lakshmibai, P. Littelmann, P. Magyar
- Mathematics
- 1998

In these notes, we explain how one can construct Standard Monomial Theory for reductive algebraic groups by using the path models of their representations and quantum groups at a root of unity. As… Expand

Degeneracy schemes, quiver schemes, and Schubert varieties

- V. Lakshmibai, P. Magyar
- Mathematics
- 1998

abstract. A result of Zelevinsky states that an orbit closure in the space of representations of the equioriented quiver of type A h is in bijection with the opposite cell in a Schubert variety of a… Expand

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