## Abstract

In [3] V. Ginzburg observed that one can realize irreducible representations of the group GL(n, ℂ) in the cohomology of certain Springer's fibers for the group GL_{d} (for all d ∈ ℕ). However, Ginzburg's construction of the action of GL(n) on this cohomology was a bit artificial (he defined the action of Chevalley generators of the Lie algebra gl_{n} on the corresponding cohomology by certain explicit correspondences, following the work of A. Beilinson, G. Lusztig and R. MacPherson ([1]), who gave a similar construction of the quantum group U_{q}(gl_{n})). In this note we give a very simple geometric definition of the action of the whole group GL(n, ℂ) on the above cohomology and simplify the results of [3].

Original language | English |
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Pages (from-to) | 195-201 |

Number of pages | 7 |

Journal | Mathematical Research Letters |

Volume | 6 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1999 |

Externally published | Yes |