E. Ragoucy
Nested Bethe ansatz for Y(gl(n)) open spin chains with diagonal boundary conditions.
Mon, 01/11/2010 - 16:01 — SomNambulAuthors: S. Belliard, E. Ragoucy
Subjects: Mathematical Physics
AbstractIn this proceeding we present the nested Bethe ansatz for open spin chains of
XXX-type, with arbitrary representations (i.e. `spins') on each site of the
chain and diagonal boundary matrices $(K^+(u),K^-(u))$. The nested Bethe anstaz
applies for a general $K^-(u)$, but a particular form of the $K^+(u)$ matrix.
We give the eigenvalues, Bethe equations and the form of the Bethe vectors for
the corresponding models. The Bethe vectors are expressed using a trace
formula.The MacMahon Master Theorem for right quantum superalgebras and higher Sugawara operators for \hat gl(m|n).
Thu, 11/19/2009 - 16:01 — SomNambulAuthors: E. Ragoucy, A. I. Molev
Subjects: Representation Theory
AbstractWe prove an analogue of the MacMahon Master Theorem for the right quantum
superalgebras. In particular, we obtain a new and simple proof of this theorem
for the right quantum algebras. In the super case the theorem is then used to
construct higher order Sugawara operators for the affine Lie superalgebra \hat
gl(m|n) in an explicit form. The operators are elements of a completed
universal enveloping algebra of \hat gl(m|n) at the critical level. They occur
as the coefficients in the expansion of a noncommutative Berezinian and as the
traces of powers of generator matrices.Scattering matrix for a general gl(2) spin chain.
Wed, 09/09/2009 - 22:08 — SomNambulAuthors: S. Belliard, N. Crampe, E. Ragoucy
Subjects: Mathematical Physics
AbstractWe study the general L_0-regular gl(2) spin chain, i.e. a chain where the
sites {i,i+L_0,i+2L_0,...} carry the same arbitrary representation (spin) of
gl(2). The basic example of such chain is obtained for L_0=2, where we recover
the alternating spin chain.Firstly, we review different known results about their integrability and
their spectrum. Secondly, we give an interpretation in terms of particles and
conjecture the scattering matrix between them.
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