Row Convex Tableaux and Bott-Samelson Varieties
作者： Sangjib Kim , Philip Foth
DOI:
关键词: Mathematics 、 Regular polygon 、 Pure mathematics 、 Monomial 、 Polynomial 、 Variety (universal algebra) 、 Discrete mathematics 、 Type (model theory) 、 Section (fiber bundle)
摘要: By using row convex tableaux, we study the section rings of Bott-Samelson varieties type A. We obtain flat deformations and standard monomial bases rings. In a separate section, investigate three dimensional variety in detail compute its Hilbert polynomial toric degenerations.
arxiv.org参考文章(12)
Peter Doubilet, Gian-Carlo Rota, Joel Stein, On the Foundations of Combinatorial Theory: IX Combinatorial Methods in Invariant Theory Studies in Applied Mathematics. ,vol. 53, pp. 185- 216 ,(1974) , 10.1002/SAPM1974533185
Bernd Sturmfels, Ezra Miller, Combinatorial Commutative Algebra ,(2004)
Michael Grossberg, Yael Karshon, Bott towers, complete integrability, and the extended character of representations Duke Mathematical Journal. ,vol. 76, pp. 23- 58 ,(1994) , 10.1215/S0012-7094-94-07602-3
Venkatramani Lakshmibai, Peter Littelmann, Peter Magyar, Standard Monomial Theory for Bott–Samelson Varieties Compositio Mathematica. ,vol. 130, pp. 293- 318 ,(2002) , 10.1023/A:1014396129323
R. Bott, H. Samelson, THE COHOMOLOGY RING OF G/T Proceedings of the National Academy of Sciences of the United States of America. ,vol. 41, pp. 490- 493 ,(1955) , 10.1073/PNAS.41.7.490
Venkatramani Lakshmibai, Peter Magyar, Standard Monomial Theory for Bott-Samelson Varieties of GL(n) Publications of The Research Institute for Mathematical Sciences. ,vol. 34, pp. 229- 248 ,(1998) , 10.2977/PRIMS/1195144694
P. Magyar, Schubert polynomials and Bott-Samelson varieties Commentarii Mathematici Helvetici. ,vol. 73, pp. 603- 636 ,(1998) , 10.1007/S000140050071
Boris Pasquier, Vanishing theorem for the cohomology of line bundles on Bott–Samelson varieties Journal of Algebra. ,vol. 323, pp. 2834- 2847 ,(2010) , 10.1016/J.JALGEBRA.2010.03.016
Brian D Taylor, A Straightening Algorithm for Row-Convex Tableaux Journal of Algebra. ,vol. 236, pp. 155- 191 ,(2001) , 10.1006/JABR.2000.8495
Mikhail Kogan, Ezra Miller, Toric degeneration of Schubert varieties and Gelfand¿Tsetlin polytopes Advances in Mathematics. ,vol. 193, pp. 1- 17 ,(2005) , 10.1016/J.AIM.2004.03.017