2,716 research outputs found
Character Formulas from Matrix Factorisations
(With an Appendix by Constantin Teleman) In the spirit of Freed, Hopkins, and
Teleman I establish an equivalence between the category of discrete series
representations of a real semisimple Lie group G and a category of equivariant
matrix factorisations on a subset of the dual of the Lie algebra, in analogy
with the situation in [FT] which treated the case when G is compact or a loop
group thereof. The equivalence is implemented by a version of the Dirac
operator used in [FHT1-3], squaring to the superpotential W defining the matrix
factorisations. Using the structure of the resulting matrix factorisation
category as developed in [FT] I deduce the Kirillov character formula for
compact Lie groups and the Rossman character formula for the discrete series of
a real semi-simple Lie group. The proofs are a calculation of Chern characters
and use the Dirac family constructed in [FHT1-3]. Indeed, the main theorems of
[FHT3] and [FT] are a categorification of the Kirillov correspondence, and this
paper establishes that this correspondence can be recovered at the level of
characters.Comment: Appendix (by Constantin Teleman) to appear in final versio
Completed K-theory and Equivariant Elliptic Cohomology
Kitchloo and Morava give a strikingly simple picture of elliptic cohomology
at the Tate curve by studying a completed version of -equivariant
-theory for spaces. I present a -equivariant version of their
construction, which is a completed version of the Freed-Hopkins-Teleman model
of -theory for local quotient groupoids and resolves the issues concerning
twisting and degree that arise in a first attempt to relate their work to
elliptic cohomology.Comment: 23 page
Strongly nonlinear convection in binary fluids: Minimal model for extended states using symmetry decomposed modes
Spatially extended stationary and traveling states in the strongly nonlinear
regime of convection in layers of binary fluid mixtures heated from below are
described by a few-mode-model. It is derived from the proper hydrodynamic
balance equations including experimentally relevant boundary conditions with a
non-standard Galerkin approximation that uses numerically obtained, symmetry
decomposed modes. Properties of the model are elucidated and compared with full
numerical solutions of the field equations.Comment: 16 pages, including 5 postscript figure
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