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 کاملStanley Symmetric Functions and Peterson Algebras
These are (mostly) expository notes for lectures on affine Stanley symmetric functions given at the Fields Institute in 2010. We focus on the algebraic and combinatorial parts of the theory. The notes contain a number of exercises and open problems. Stanley symmetric functions are a family {Fw | w ∈ Sn} of symmetric functions indexed by permutations. They were invented by Stanley [Sta] to enume...
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].
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2020
ISSN: 0012-365X
DOI: 10.1016/j.disc.2019.111778