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POLYNOMIALS FOR SYMMETRIC ORBIT CLOSURES IN THE FLAG VARIETY

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Abstract

In [WY] we introduced polynomial representatives of cohomology classes of orbit closures in the flag variety, for the symmetric pair (GL p+q , GL p × GL q ). We present analogous results for the remaining symmetric pairs of the form (GL n , K), i.e., (GL n , O n ) and (GL 2n , Sp 2n ). We establish “well-definedness” of certain representatives from [Wy1]. It is also shown that the representatives have the combinatorial properties of nonnegativity and stability. Moreover, we give some extensions to equivariant K-theory.

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Authors and Affiliations

  1. Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA

    B. WYSER & A. YONG

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  1. B. WYSER
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  2. A. YONG
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Correspondence to A. YONG.

Additional information

(B. WYSER) Supported by NSF International Research Fellowship 1159045 and hosted by Institut Fourier in Grenoble.

(A. YONG) Supported by NSF grant DMS 1201595 and the Helen Corley Petit endowment at UIUC.

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WYSER, B., YONG, A. POLYNOMIALS FOR SYMMETRIC ORBIT CLOSURES IN THE FLAG VARIETY. Transformation Groups 22, 267–290 (2017). https://doi.org/10.1007/s00031-016-9381-x

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  • DOI: https://doi.org/10.1007/s00031-016-9381-x

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