Geodesic
Schubert calculus and representations of the general linear group
Mukhin, E.1 ; Tarasov, V.2 ; Varchenko, A.3
1 Department of Mathematical Sciences, Indiana University, Purdue University Indianapolis, 402 North Blackford Street, Indianapolis, Indiana 46202-3216
2 St. Petersburg Branch of Steklov Mathematical Institute, Fontanka 27, St. Peters- burg, 191023, Russia
3 Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599-3250
Journal of the American Mathematical Society, Tome 22 (2009) no. 4, pp. 909-940

Voir la notice de l'article provenant de la source American Mathematical Society

We construct a canonical isomorphism between the Bethe algebra acting on a multiplicity space of a tensor product of evaluation $\mathfrak {gl}_N[t]$-modules and the scheme-theoretic intersection of suitable Schubert varieties. Moreover, we prove that the multiplicity space as a module over the Bethe algebra is isomorphic to the coregular representation of the scheme-theoretic intersection. In particular, this result implies the simplicity of the spectrum of the Bethe algebra for real values of evaluation parameters and the transversality of the intersection of the corresponding Schubert varieties.
DOI : 10.1090/S0894-0347-09-00640-7

Mukhin, E. 1 ; Tarasov, V. 2 ; Varchenko, A. 3

1 Department of Mathematical Sciences, Indiana University, Purdue University Indianapolis, 402 North Blackford Street, Indianapolis, Indiana 46202-3216
2 St. Petersburg Branch of Steklov Mathematical Institute, Fontanka 27, St. Peters- burg, 191023, Russia
3 Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599-3250 
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Mukhin, E.; Tarasov, V.; Varchenko, A. Schubert calculus and representations of the general linear group. Journal of the American Mathematical Society, Tome 22 (2009) no. 4, pp. 909-940. doi: 10.1090/S0894-0347-09-00640-7

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