Schubert calculus and representations of the general linear group

By E. Mukhin, V. Tarasov, A. Varchenko. 2007

138 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8aae5f1e8fd0f4f5bf8779b812c60c32ac8f110a

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In Algebra and Number Theory

1. V. Tarasov
2. Alexandre Eremenko
3. Andrei Gabrielov

In Geometry and Topology

1. V. Tarasov
2. Alexandre Eremenko
3. Andrei Gabrielov
4. A. Varchenko
5. E. Mukhin

In Mathematical Physics

1. V. Tarasov
2. Alexandre Eremenko
3. Andrei Gabrielov

Citations in the corpus

• Metrics with conic singularities and spherical polygons (2014, methodology): “Also, this problem is equivalent to diagonalization of commuting Hamiltonians for the quantum Gaudin model by the Bethe ansatz method [11], [22], [24].”