On Multiplicities of Points on Schubert Varieties in Graßmannians II

Autor:	C. Krattenthaler
Rok vydání:	2005
Předmět:	Schubert variety Weyl group Algebra and Number Theory Conjecture Tangent cone Schubert calculus Schubert polynomial Lattice (discrete subgroup) Combinatorics symbols.namesake symbols Discrete Mathematics and Combinatorics Mathematics Hilbert–Poincaré series
Zdroj:	Journal of Algebraic Combinatorics. 22:273-288
ISSN:	1572-9192 0925-9899
DOI:	10.1007/s10801-005-4527-2
Popis:	We prove a conjecture by Kreiman and Lakshmibai on a combinatorial description of multiplicities of points on Schubert varieties in Graβmannian in terms of certain sets of reflections in the corresponding Weyl group. The proof is accomplished by relating these sets of reflections to the author's previous combinatorial interpretation of these multiplicities in terms of non-intersecting lattice paths (Seminaire Lotharingien Combin. 45 (2001), Article B45c). Moreover, we provide a compact formula for the Hilbert series of the tangent cone to a Schubert variety in a Graβmannian assuming the truth of another conjecture of Kreiman and Lakshmibai.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::1f2deb20d618a1119673e84beab45e65 https://doi.org/10.1007/s10801-005-4527-2 Zobrazit plný text záznamu Full text from SpringerLink