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Marberg, Eric

A symplectic refinement of shifted Hecke insertion. (English) Zbl 1435.05236

J. Comb. Theory, Ser. A 173, Article ID 105216, 50 p. (2020).
Summary: A. S. Buch et al. [Math. Ann. 340, No. 2, 359–382 (2008; Zbl 1157.14036)] defined Hecke insertion to formulate a combinatorial rule for the expansion of the stable Grothendieck polynomials \(G_\pi\) indexed by permutations in the basis of stable Grothendieck polynomials \(G_\lambda\) indexed by partitions. Patrias and Pylyavskyy introduced a shifted analogue of Hecke insertion whose natural domain is the set of maximal chains in a weak order on orbit closures of the orthogonal group acting on the complete flag variety. We construct a generalization of shifted Hecke insertion for maximal chains in an analogous weak order on orbit closures of the symplectic group. As an application, we identify a combinatorial rule for the expansion of “orthogonal” and “symplectic” shifted analogues of \(G_\pi\) in Ikeda and Naruse’s basis of \(K\)-theoretic Schur \(P\)-functions.

Cited in 1 Review
Cited in 14 Documents

MSC:

05E14 Combinatorial aspects of algebraic geometry
14M15 Grassmannians, Schubert varieties, flag manifolds

Keywords:

symmetric groups; Grothendieck polynomials; Hecke insertion; Schur \(P\)-functions; flag varieties

Citations:

Zbl 1157.14036
PDFBibTeX XMLCite
\textit{E. Marberg}, J. Comb. Theory, Ser. A 173, Article ID 105216, 50 p. (2020; Zbl 1435.05236)
Full Text: DOI arXiv

References:

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