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• W1617055173 abstract "In this paper we explicitly compute all Littlewood-Richardson coefficients for semisimple or Kac-Moody groups G, that is, the structure coefficients of the cohomology algebra H^*(G/P), where P is a parabolic subgroup of G. These coefficients are of importance in enumerative geometry, algebraic combinatorics and representation theory. Our formula for the Littlewood-Richardson coefficients is given in terms of the Cartan matrix and the Weyl group of G. However, if some off-diagonal entries of the Cartan matrix are 0 or -1, the formula may contain negative summands. On the other hand, if the Cartan matrix satisfies $a_{ij}a_{ji}ge 4$ for all $i,j$, then each summand in our formula is nonnegative that implies nonnegativity of all Littlewood-Richardson coefficients. We extend this and other results to the structure coefficients of the T-equivariant cohomology of flag varieties G/P and Bott-Samelson varieties Gamma_ii(G)." @default.
• W1617055173 created "2016-06-24" @default.
• W1617055173 creator A5028806356 @default.
• W1617055173 creator A5063931803 @default.
• W1617055173 date "2015-10-01" @default.
• W1617055173 modified "2023-09-29" @default.
• W1617055173 title "Littlewood–Richardson coefficients for reflection groups" @default.
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• W1617055173 doi "https://doi.org/10.1016/j.aim.2015.07.017" @default.
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