Geodesic
Cohomology of a flag variety as a~Bethe algebra
Funkcionalʹnyj analiz i ego priloženiâ, Tome 45 (2011) no. 4, pp. 16-31

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We interpret the equivariant cohomology $H^*_{GL_n}(\mathcal{F}_{\boldsymbol\lambda},mathbb{C})$ of a partial flag variety $\mathcal{F}_{\boldsymbol\lambda}$ parametrizing chains of subspaces $0=F_0\subset F_1\subset\dots\subset F_N=\mathbb{C}^n$, $\dim F_i/F_{i-1}=\lambda_i$, as the Bethe algebra $\mathcal{B}^\infty(\mathcal{V}^\pm_{\boldsymbol\lambda})$ of the $\mathfrak{gl}_N$-weight subspace $\mathcal{V}^\pm_{\boldsymbol\lambda}$ of a $\mathfrak{gl}_N[t]$-module $\mathcal{V}^\pm$.
Keywords: Gaudin model, Bethe algebra, cohomology of flag varieties. 
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     author = {A. N. Varchenko and R. Rim\'anyi and V. O. Tarasov and V. V. Schechtman},
     title = {Cohomology of a flag variety as {a~Bethe} algebra},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {16--31},
     publisher = {mathdoc},
     volume = {45},
     number = {4},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2011_45_4_a1/}
}
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A. N. Varchenko; R. Rimányi; V. O. Tarasov; V. V. Schechtman. Cohomology of a flag variety as a~Bethe algebra. Funkcionalʹnyj analiz i ego priloženiâ, Tome 45 (2011) no. 4, pp. 16-31. http://geodesic.mathdoc.fr/item/FAA_2011_45_4_a1/