14,476 research outputs found
A mixed hook-length formula for affine Hecke algebras
Consider the affine Hecke algebra corresponding to the group
over a -adic field with the residue field of cardinality . Regard
as an associative algebra over the field . Consider the -module
induced from the tensor product of the evaluation modules over the algebras
and . The module depends on two partitions of and
of , and on two non-zero elements of the field . There is a
canonical operator acting on , it corresponds to the trigonometric
-matrix. The algebra contains the finite dimensional Hecke algebra
of rank as a subalgebra, and the operator commutes with the action of
this subalgebra on . Under this action, decomposes into irreducible
subspaces according to the Littlewood-Richardson rule. We compute the
eigenvalues of , corresponding to certain multiplicity-free irreducible
components of . In particular, we give a formula for the ratio of two
eigenvalues of , corresponding to the ``highest'' and the ``lowest''
components. As an application, we derive the well known -analogue of the
hook-length formula for the number of standard tableaux of shape .Comment: 36 pages, final versio
Partition Functions for Maxwell Theory on the Five-torus and for the Fivebrane on S1XT5
We compute the partition function of five-dimensional abelian gauge theory on
a five-torus T5 with a general flat metric using the Dirac method of quantizing
with constraints. We compare this with the partition function of a single
fivebrane compactified on S1 times T5, which is obtained from the six-torus
calculation of Dolan and Nappi. The radius R1 of the circle S1 is set to the
dimensionful gauge coupling constant g^2= 4\pi^2 R1. We find the two partition
functions are equal only in the limit where R1 is small relative to T5, a limit
which removes the Kaluza-Klein modes from the 6d sum. This suggests the 6d
N=(2,0) tensor theory on a circle is an ultraviolet completion of the 5d gauge
theory, rather than an exact quantum equivalence.Comment: v4, 37 pages, published versio
- …