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Gelfand–Tsetlin algebras and cohomology rings of Laumon spaces

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Abstract

Laumon moduli spaces are certain smooth closures of the moduli spaces of maps from the projective line to the flag variety of GL n . We calculate the equivariant cohomology rings of the Laumon moduli spaces in terms of Gelfand–Tsetlin subalgebra of U(gl n ) and formulate a conjectural answer for the small quantum cohomology rings in terms of certain commutative shift of argument subalgebras of U(gl n ).

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Authors and Affiliations

  1. Landau Institute for Theoretical Physics, Kosygina st 2, 117940, Moscow, Russia

    Boris Feigin

  2. Department of Mathematics, IMU, IITP and State University Higher School of Economics, 20 Myasnitskaya st, 101000, Moscow, Russia

    Michael Finkelberg

  3. Department of Mathematics, Yale University, PO Box 208283, New Haven, CT, 06520, USA

    Igor Frenkel

  4. Department of Mathematics, Institute for the Information Transmission Problems and State University Higher School of Economics, 20 Myasnitskaya st, 101000, Moscow, Russia

    Leonid Rybnikov

Authors
  1. Boris Feigin
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  2. Michael Finkelberg
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  3. Igor Frenkel
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  4. Leonid Rybnikov
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Corresponding author

Correspondence to Michael Finkelberg.

Additional information

To the memory of Izrail Moiseevich Gelfand

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Feigin, B., Finkelberg, M., Frenkel, I. et al. Gelfand–Tsetlin algebras and cohomology rings of Laumon spaces. Sel. Math. New Ser. 17, 337–361 (2011). https://doi.org/10.1007/s00029-010-0045-8

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