Schubert calculus and representations of general linear group

Details Schubert calculus and representations of general linear group Schubert calculus and representations of general linear group

2007-11-26

arxiv.org/abs/0711.4079v1

Mathematics

Quantum Algebra

Latex, 32 pages

Scientific paper

We construct a canonical isomorphism between the Bethe algebra acting on a multiplicity space of a tensor product of evaluation 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.

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