Shifted K-theoretic Poirier-reutenauer Bialgebra
نویسندگان
چکیده
We use shifted K-theoretic jeu de taquin to show that the weak K-Knuth equivalence relation introduced in [3] is compatible with the shifted Hecke insertion algorithm introduced in [9]. This allows us to define a K-theoretic analogue of the shifted Poirier-Reutenauer Hopf bialgebra developed by [6]. From this, we derive a new symmetric function that corresponds to K-theory of OG(n, 2n+ 1) and prove a Littlewood-Richardson rule for these symmetric functions.
منابع مشابه
Shifted K-theoretic Poirier-reutenauer Algebra
Poirier and Reutenauer defined a Hopf algebra on the Z-span of all standard Young tableaux in [10], which is later studied in [4, 11]. The Robinson-Schensted-Knuth insertion was used to relate the bialgebra to Schur functions. Schur function is a class of symmetric functions that can be determined by the summation of all semistandard Young tableaux of shape . With the help of the PR-bialgebra, ...
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