52,168 research outputs found
A Demazure crystal construction for Schubert polynomials
Stanley symmetric functions are the stable limits of Schubert polynomials. In
this paper, we show that, conversely, Schubert polynomials are Demazure
truncations of Stanley symmetric functions. This parallels the relationship
between Schur functions and Demazure characters for the general linear group.
We establish this connection by imposing a Demazure crystal structure on key
tableaux, recently introduced by the first author in connection with Demazure
characters and Schubert polynomials, and linking this to the type A crystal
structure on reduced word factorizations, recently introduced by Morse and the
second author in connection with Stanley symmetric functions.Comment: 18 pages, 16 figures; version 2: references added and update
A matrix model for a quantum hall droplet with manifest particle-hole symmetry
We find that a gauged matrix model of rectangular fermionic matrices (a
matrix version of the fermion harmonic oscillator) realizes a quantum hall
droplet with manifest particle-hole symmetry. The droplet consists of free
fermions on the topology of a sphere. It is also possible to deform the
Hamiltonian by double trace operators, and we argue that this device can
produce two body potentials which might lead the system to realize a fractional
quantum hall state on the sphere. We also argue that a single gauged fermionic
quantum mechanics of hermitian matrices realizes a droplet with an edge that
has CFT on it.Comment: 25 pages, uses JHEP format, young.sty (included). v2: Updated
references, typos correcte
The Morphology of N=6 Chern-Simons Theory
We tabulate various properties of the language of N=6 Chern-Simons Theory, in
the sense of Polyakov. Specifically we enumerate and compute character formulas
for all syllables of up to four letters, i.e. all irreducible representations
of OSp(6|4) built from up to four fundamental fields of the ABJM theory. We
also present all tensor product decompositions for up to four singletons and
list the (cyclically invariant) four-letter words, which correspond to
single-trace operators of length four. As an application of these results we
use the two-loop dilatation operator to compute the leading correction to the
Hagedorn temperature of the weakly-coupled planar ABJM theory on R \times S^2.Comment: 41 pages, 1 figure; v2: minor correction
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