Jiuzu Hong

Polynomial functors and categorifications of Fock space II

We categorify various Fock space representations on the algebra of symmetric functions via the category of polynomial functors. In a prequel, we used polynomial functors to categorify the Fock space representations of type A Kac-Moody algebras. In the current work we define a representation of the Heisenberg algebra on the category of polynomial functors, and show that it categorifies the Fock space representation. We also categorify the commuting actions of the affine Lie algebras and the Heisenberg algebras on Fock space. Moreover, we study the relationship between these categorifications and Schur-Weyl duality. The duality is formulated as a functor from the category of polynomial functors to the category of linear species. The category of linear species is known to carry actions of the Kac-Moody algebra and the Heisenberg algebra. We prove that Schur-Weyl duality is a morphism of these categorification structures.

Mirkovic-Vilonen cycles and polytopes for a symmetric pair

Let

Tensor invariants, saturation problems, and Dynkin automorphisms

G

Generalized semi-invariant distributions on p-adic spaces

be a connected, simply-connected, and almost simple algebraic group, and let

POLYNOMIAL REPRESENTATIONS OF GENERAL LINEAR GROUPS AND CATEGORIFICATIONS OF FOCK SPACE

\sigma

Almost prime coordinates for anisotropic and thin pythagorean orbits

be a Dynkin automorphism on

Quantum polynomial functors

G

Conformal blocks, Verlinde formula and diagram automorphisms

. In this paper, we get a bijection between the set of

Polynomial functors and categorifications of Fock space II: Schur-Weyl duality

\st

Conformal blocks for Galois covers of algebraic curves

-invariant MV cycles (polytopes) for