Abstract
We interpret the equivariant cohomology \(H_{GL_n }^* \)(ℱ λ ,ℂ) of a partial flag variety ℱ λ parametrizing chains of subspaces 0 = F 0 ⊂ F 1 ⊂ … ⊂ F N = ℂn, dimF i /F i−1 = λ i , as the Bethe algebra of the -weight subspace of a [t]-module .
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Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 45, No. 4, pp. 16–31, 2011
Original Russian Text Copyright © by R. Rimányi, V. Schechtman, V. Tarasov, and A. Varchenko
To the memory of V. I. Arnold
The first author is supported in part by NSA grant CON:H98230-10-1-0171. The third author is supported in part by NSF grant DMS-0901616. The fourth author is supported in part by NSF grant DMS-0555327.
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Rimányi, R., Schechtman, V., Tarasov, V. et al. Cohomology of a flag variety as a Bethe algebra. Funct Anal Its Appl 45, 252–264 (2011). https://doi.org/10.1007/s10688-011-0027-4
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DOI: https://doi.org/10.1007/s10688-011-0027-4