A family of reductions for Schubert intersection problems
H. Bercovici1
, W.S. Li2
and D. Timotin3
1Department of Mathematics, Indiana University, Bloomington, IN 47405, USA
2Simion Stoilow Institute of Mathematics of the Romanian Academy, PO Box 1-764, Bucharest 014700, Romania
2Simion Stoilow Institute of Mathematics of the Romanian Academy, PO Box 1-764, Bucharest 014700, Romania
DOI: 10.1007/s10801-010-0261-5
Abstract
We produce a family of reductions for Schubert intersection problems whose applicability is checked by calculating a linear combination of the dimensions involved. These reductions do not alter the Littlewood-Richardson coefficient, and this fact is connected to known multiplicative properties of these coefficients.
Pages: 609–649
Keywords: keywords Schubert variety; Littlewood-Richardson rule; puzzle; tree; measure
Full Text: PDF
References
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2. Buch, A.S.: The saturation conjecture (after A. Knutson and T. Tao). With an appendage by William Fulton. Enseign. Math. (2) 46(1-2), 43-60 (2000)
3. Collins, B., Dykema, K.: On a reduction procedure for Horn inequalities in finite von Neumann algebras. Oper. Matrices 3, 1-40 (2009)
4. Danilov, V.I., Koshevoy, G.A.: Discrete convexity and Hermitian matrices. Tr. Mat. Inst. Steklova 241, 68-89 (2003); translation in Proc. Steklov Inst. Math. 241, 58-78 (2003)
5. Derksen, H., Weyman, J.: The combinatorics of quiver representations, preprint, 2006,
6. Fulton, W.: Young Tableaux. Cambridge University Press, Cambridge (1997)
7. King, R.C., Tollu, C., Christophe, F.: Factorisation of Littlewood-Richardson coefficients. J. Combin.
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