425 research outputs found
Central extensions of classical and quantum q-Viraroso algebras
We investigate the central extensions of the q-deformed (classical and
quantum) Virasoro algebras constructed from the elliptic quantum algebra
A_{q,p}[sl(N)_c]. After establishing the expressions of the cocycle conditions,
we solve them, both in the classical and in the quantum case (for sl(2)). We
find that the consistent central extensions are much more general that those
found previously in the literature.Comment: Latex2e, needs amsfonts and amssymb package
Deformed W_N algebras from elliptic sl(N) algebras
We extend to the sl(N) case the results that we previously obtained on the
construction of W_{q,p} algebras from the elliptic algebra
A_{q,p}(\hat{sl}(2)_c). The elliptic algebra A_{q,p}(\hat{sl}(N)_c) at the
critical level c=-N has an extended center containing trace-like operators
t(z). Families of Poisson structures indexed by N(N-1)/2 integers, defining
q-deformations of the W_N algebra, are constructed. The operators t(z) also
close an exchange algebra when (-p^1/2)^{NM} = q^{-c-N} for M in Z. It becomes
Abelian when in addition p=q^{Nh} where h is a non-zero integer. The Poisson
structures obtained in these classical limits contain different q-deformed W_N
algebras depending on the parity of h, characterizing the exchange structures
at p \ne q^{Nh} as new W_{q,p}(sl(N)) algebras.Comment: LaTeX2e Document - packages subeqn,amsfonts,amssymb - 30 page
From quantum to elliptic algebras
It is shown that the elliptic algebra at the
critical level c=-2 has a multidimensional center containing some trace-like
operators t(z). A family of Poisson structures indexed by a non-negative
integer and containing the q-deformed Virasoro algebra is constructed on this
center. We show also that t(z) close an exchange algebra when p^m=q^{c+2} for m
integer, they commute when in addition p=q^{2k} for k integer non-zero, and
they belong to the center of when k is odd. The
Poisson structures obtained for t(z) in these classical limits contain the
q-deformed Virasoro algebra, characterizing the structures at generic values of
p, q and m as new algebras.Comment: LaTeX2e Document - packages subeqn,amsfont
Universal construction of W_{p,q} algebras
We present a direct construction of abstract generators for q-deformed W_N
algebras. This procedure hinges upon a twisted trace formula for the elliptic
algebra A_{q,p}(sl(N)_c) generalizing the previously known formulae for quantum
groups.Comment: packages amsfonts, amssym
Spin chains from dynamical quadratic algebras
We present a construction of integrable quantum spin chains where local
spin-spin interactions are weighted by ``position''-dependent potential
containing abelian non-local spin dependance. This construction applies to the
previously defined three general quadratic reflection-type algebras:
respectively non-dynamical, semidynamical, fully dynamical.Comment: 12 pages, no figures; v2: corrected formulas of the last sectio
Implementation pathway report: Community Resource Person An intervention by the Technical Support Unit Uttar Pradesh, India, February 2015
A report describing the methodology behind an implementation pathway for the Community Resource Person innovation being implemented by the Technical Support Unit (a large-scale collaboration between the Bill & Melinda Gates Foundation and the Uttar Pradesh government) in Uttar Pradesh, India
Parametrization of semi-dynamical quantum reflection algebra
We construct sets of structure matrices for the semi-dynamical reflection
algebra, solving the Yang-Baxter type consistency equations extended by the
action of an automorphism of the auxiliary space. These solutions are
parametrized by dynamical conjugation matrices, Drinfel'd twist representations
and quantum non-dynamical -matrices. They yield factorized forms for the
monodromy matrices.Comment: LaTeX, 24 pages. Misprints corrected, comments added in Conclusion on
construction of Hamiltonian
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
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
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