منابع مشابه
Affine Stanley Symmetric Functions
We define a new family F̃w(X) of generating functions for w ∈ S̃n which are affine analogues of Stanley symmetric functions. We establish basic properties of these functions such as their symmetry and conjecture certain positivity properties. As an application, we relate these functions to the k-Schur functions of Lapointe, Lascoux and Morse as well as the cylindric Schur functions of Postnikov. ...
متن کاملAffine Stanley symmetric functions for classical types
We introduce affine Stanley symmetric functions for the special orthogonal groups, a class of symmetric functions that model the cohomology of the affine Grassmannian, continuing the work of Lam and Lam, Schilling, and Shimozono on the special linear and symplectic groups, respectively. For the odd orthogonal groups, a Hopf-algebra isomorphism is given, identifying (co)homology Schubert classes...
متن کاملAFFINE STANLEY SYMMETRIC FUNCTIONS By THOMAS LAM
We define a new family F̃w(X) of generating functions for w ∈ S̃n which are affine analogues of Stanley symmetric functions. We establish basic properties of these functions including symmetry, dominance and conjugation. We conjecture certain positivity properties in terms of a subfamily of symmetric functions called affine Schur functions. As applications, we show how affine Stanley symmetric fu...
متن کاملA Little Bijection for Affine Stanley Symmetric Functions
Little [Adv. Math. 174 (2003), 236–253] developed a combinatorial algorithm to study the Schur-positivity of Stanley symmetric functions and the Lascoux–Schützenberger tree. We generalize this algorithm to affine Stanley symmetric functions, which were introduced recently in [T. Lam: “Affine Stanley symmetric functions,” Amer. J. Math., to appear].
متن کاملDiagrams of affine permutations , balanced labellings , and affine Stanley symmetric functions (
We study the diagrams of affine permutations and their balanced labellings. As in the finite case, which was investigated by Fomin, Greene, Reiner, and Shimozono, the balanced labellings give a natural encoding of reduced decompositions of affine permutations. In fact, we show that the sum of weight monomials of the column strict balanced labellings is the affine Stanley symmetric function defi...
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ژورنال
عنوان ژورنال: American Journal of Mathematics
سال: 2006
ISSN: 1080-6377
DOI: 10.1353/ajm.2006.0045