312,218 research outputs found
Schur-Weyl duality for orthogonal groups
We prove Schur--Weyl duality between the Brauer algebra
and the orthogonal group over an arbitrary infinite field of odd
characteristic. If is even, we show that each connected component of the
orthogonal monoid is a normal variety; this implies that the orthogonal Schur
algebra associated to the identity component is a generalized Schur algebra. As
an application of the main result, an explicit and characteristic-free
description of the annihilator of -tensor space in the
Brauer algebra is also given.Comment: 35 pages; to appear in Proc. L.M.
Meanders and the Temperley-Lieb algebra
The statistics of meanders is studied in connection with the Temperley-Lieb
algebra. Each (multi-component) meander corresponds to a pair of reduced
elements of the algebra. The assignment of a weight per connected component
of meander translates into a bilinear form on the algebra, with a Gram matrix
encoding the fine structure of meander numbers. Here, we calculate the
associated Gram determinant as a function of , and make use of the
orthogonalization process to derive alternative expressions for meander numbers
as sums over correlated random walks.Comment: 85p, uuencoded, uses harvmac (l mode) and epsf, 88 figure
The lower central series of the symplectic quotient of a free associative algebra
We study the lower central series filtration L_k for a symplectic quotient
A=A_{2n}/ of the free algebra A_{2n} on 2n generators, where w=\sum
[x_i,x_{i+n}]. We construct an action of the Lie algebra H_{2n} of Hamiltonian
vector fields on the associated graded components of the filtration, and use
this action to give a complete description of the reduced first component
\bar{B}_1(A)= A/(L_2 + AL_3) and the second component B_2=L_2/L_3, and we
conjecture a description for the third component B_3=L_3/L_4.Comment: Corrected formulas for singular vectors, implemented referee
suggestion
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