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ROW CONVEX TABLEAUX AND BOTT–SAMELSON VARIETIES

Part of: Algebraic combinatorics Special varieties

Published online by Cambridge University Press:  23 October 2014

PHILIP FOTH  and
SANGJIB KIM
PHILIP FOTH
Affiliation:
Champlain St. Lawrence College, Quebec, Canada G1V 4K2 email phfoth@gmail.com
SANGJIB KIM*
Affiliation:
Department of Mathematics, Ewha Womans University, Seoul 151-892, South Korea email sk23@ewha.ac.kr
*
✉sk23@ewha.ac.kr
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Abstract

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By using row convex tableaux, we study the section rings of Bott–Samelson varieties of type A. We obtain flat deformations and standard monomial type bases of the section rings. In a separate section, we investigate a three-dimensional Bott–Samelson variety in detail and compute its Hilbert polynomial and toric degenerations.

Keywords

Bott–Samelson varietystraight tableauxtoric deformations

MSC classification

Secondary: 14M15: Grassmannians, Schubert varieties, flag manifolds 05E40: Combinatorial aspects of commutative algebra 05E10: Combinatorial aspects of representation theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 97 , Issue 3 , December 2014 , pp. 315 - 330
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

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