1 k - Schur functions and affine Schubert calculus
نویسندگان
چکیده
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. ...
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We construct the Schubert basis of the torus-equivariant K-homology of the affine Grassmannian of a simple algebraic group G, using the K-theoretic NilHecke ring of Kostant and Kumar. This is the K-theoretic analogue of a construction of Peterson in equivariant homology. For the case where G= SLn, the K-homology of the affine Grassmannian is identified with a sub-Hopf algebra of the ring of sym...
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Confirming a conjecture of Mark Shimozono, we identify polynomial representatives for the Schubert classes of the affine Grassmannian as the k-Schur functions in homology and affine Schur functions in cohomology. Our results rely on Kostant and Kumar’s nilHecke ring, work of Peterson on the homology of based loops on a compact group, and earlier work of ours on non-commutative k-Schur functions.
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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...
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The main purpose of this paper is to show that the multiplication of a Schubert polynomial of finite type A by a Schur function can be understood from the multiplication in the space of dual k-Schur functions. Using earlier work by the second author, we encode both problems by means of quasisymmetric functions. On the Schubert vs. Schur side, we study the r-Bruhat order given by Bergeron-Sottil...
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تاریخ انتشار 2013