Quasiparabolic sets and Stanley symmetric functions for affine fixed-point-free involutions

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. ...

Affine 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...

AFFINE 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...

Fixed Point Free Involutions and Equivariant Maps

1. Preliminaries. We are concerned with involutions without fixed points, together with equivariant maps connecting such involutions. An involution T is a homeomorphism of period 2 of a Hausdorff space X onto itself; that is, T(x) = x for all x £ X . There is associated with an involution T on X the orbit space X/T, obtained by identifying x with T(x) for all x G Z . Denote by v\ X—+X/T the dec...

Fixed Point Sets of Involutions on Spheres