Expansion of $k$-Schur functions for maximal rectangles within the affine nilCoxeter algebra
نویسندگان
چکیده
منابع مشابه
Expansions of k-Schur Functions in the Affine nilCoxeter Algebra
We give a type free formula for the expansion of k-Schur functions indexed by fundamental coweights within the affine nilCoxeter algebra. Explicit combinatorics are developed in affine type C.
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We prove that the Lam-Shimozono “down operator” on the affine Weyl group induces a derivation of the affine Fomin-Stanley subalgebra of the affine nilCoxeter algebra. We use this to verify a conjecture of Berg, Bergeron, Pon and Zabrocki describing the expansion of k-Schur functions of “near rectangles” in the affine nilCoxeter algebra. Consequently, we obtain a combinatorial interpretation of ...
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Formulas are obtained that express the Schur S-functions indexed by Young diagrams of rectangular shape as linear combinations of “mixed” products of Schur’s Sand Q-functions. The proof is achieved by using representations of the affine Lie algebra of type A (1) 1 . A realization of the basic representation that is of “D (2) 2 ”-type plays the central role.
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ژورنال
عنوان ژورنال: Journal of Combinatorics
سال: 2012
ISSN: 2156-3527,2150-959X
DOI: 10.4310/joc.2012.v3.n3.a9