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Singular Loci of Schubert Varieties
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 andExpand
Criterion for smoothness of Schubert varieties in Sl(n)/B
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 theExpand
Degenerations of flag and Schubert varieties to toric varieties
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
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 theExpand
Standard Monomial Theory for Bott–Samelson Varieties
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 theExpand
Equivariant Giambelli and determinantal restriction formulas for the Grassmannian
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 cohomologyExpand
Standard Monomial Theory: Invariant Theoretic Approach
Generalities on algebraic varieties.- Generalities on algebraic groups.- Grassmannian.- Determinantal varieties.- Symplectic Grassmannian.- Orthogonal Grassmannian.- The standard monomial theoreticExpand
Standard Monomial Theory and applications
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. AsExpand
Degeneracy schemes, quiver schemes, and Schubert varieties
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 aExpand