2,324 research outputs found
Coxeter group actions on the complement of hyperplanes and special involutions
We consider both standard and twisted action of a (real) Coxeter group G on
the complement M_G to the complexified reflection hyperplanes by combining the
reflections with complex conjugation. We introduce a natural geometric class of
special involutions in G and give explicit formulae which describe both actions
on the total cohomology H(M_G,C) in terms of these involutions. As a corollary
we prove that the corresponding twisted representation is regular only for the
symmetric group S_n, the Weyl groups of type D_{2m+1}, E_6 and dihedral groups
I_2 (2k+1) and that the standard action has no anti-invariants. We discuss also
the relations with the cohomology of generalised braid groups.Comment: 11 page
Elliptic quantum groups and Ruijsenaars models
We construct symmetric and exterior powers of the vector representation of
the elliptic quantum groups . The corresponding transfer
matrices give rise to various integrable difference equations which could be
solved in principle by the nested Bethe ansatz method. In special cases we
recover the Ruijsenaars systems of commuting difference operators.Comment: 15 pages, late
Polynomial solutions of the Knizhnik-Zamolodchikov equations and Schur-Weyl duality
An integral formula for the solutions of Knizhnik-Zamolodchikov (KZ) equation
with values in an arbitrary irreducible representation of the symmetric group
S_N is presented for integer values of the parameter. The corresponding
integrals can be computed effectively as certain iterated residues determined
by a given Young diagram and give polynomials with integer coefficients. The
derivation is based on Schur-Weyl duality and the results of Matsuo on the
original SU(n) KZ equation. The duality between the spaces of solutions with
parameters m and -m is discussed in relation with the intersection pairing in
the corresponding homology groups.Comment: 14 pages, reference adde
Gaudin subalgebras and wonderful models
Gaudin hamiltonians form families of r-dimensional abelian Lie subalgebras of
the holonomy Lie algebra of the arrangement of reflection hyperplanes of a
Coxeter group of rank r. We consider the set of principal Gaudin subalgebras,
which is the closure in the appropriate Grassmannian of the set of spans of
Gaudin hamiltonians. We show that principal Gaudin subalgebras form a smooth
projective variety isomorphic to the De Concini-Procesi compactification of the
projectivized complement of the arrangement of reflection hyperplanes.Comment: 13 pages, 2 figures; added detailed description of the B_2 and B_3
cases in the new versio
Efficacy and Safety Of Radiation Synovectomy with Yttrium-90
In this long term retrospective study of radiation synovectomy with Yttrium-90 (Y90), we evaluated the results of 164 applications in 82 patients with RA, OA with synovitis, ankylosing spondylitis and psoriatic arthritis. Radiation synovectomy with Y90 has an overall success rate of approximately 50% and is therefore an effective alternative to surgical synovectomy in chronic synovitis which fails to respond to conservative treatment. Elbow and knee responded significantly better than shoulder and ankle joints. Patients with radiological stages from 0 to 2 showed a significantly better success rate than those with stage 3 changes. In responders, repeat therapy for recurrence of symptoms or treatment of a symptomatic corresponding symmetrical joint is advisable. Repeat therapy in a previous non-responder is associated with an unacceptably high failure rate. Therefore, when a joint fails to respond after 6 months, arthroscopy should be performed to evaluate further treatment procedures. A successful result was found in only 11 of 25 joints treated with arthroscopic synovectomy followed by radiation synovectomy within 2 weeks, indicating no benefit of this combination
Quantum Dynamical - Matrix with Spectral Parameter from Fusion
A quantum dynamical -matrix with spectral parameter is constructed
by fusion procedure. This spin-1 -matrix is connected with Lie
algebra and does not satisfy the condition of translation invariance.Comment: 6 pages, LaTeX, no figure
Polynomial Solutions of the Knizhnik-Zamolodchikov Equations and Schur-Weyl Duality
An integral formula for the solutions of Knizhnik-Zamolodchikov (KZ) equation with values in an arbitrary irreducible representation of the symmetric group SN is presented for integer values of the parameter. The corresponding integrals can be computed effectively as certain iterated residues determined by a given Young diagram and give polynomials with integer coefficients. The derivation is based on Schur-Weyl duality and the results of Matsuo on the original SU(n) KZ equation. The duality between the spaces of solutions with parameters m and −m is discussed in relation with the intersection pairing in the corresponding homology group
BAKER-AKHIEZER FUNCTION AS ITERATED RESIDUE AND SELBERG-TYPE INTEGRAL
A simple integral formula as an iterated residue is presented for the Baker-Akhiezer function related to An-type root system in both the rational and trigonometric cases. We present also a formula for the Baker-Akhiezer function as a Selberg-type integral and generalise it to the deformed An,1-case. These formulas can be interpreted as new cases of explicit evaluation of Selberg-type integral
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