41 research outputs found
Diagonal reduction algebras of \gl type
Several general properties, concerning reduction algebras - rings of
definition and algorithmic efficiency of the set of ordering relations - are
discussed. For the reduction algebras, related to the diagonal embedding of the
Lie algebra into , we establish a stabilization
phenomenon and list the complete sets of defining relations.Comment: 24 pages, no figure
On Inflation Rules for Mosseri-Sadoc Tilings
We give the inflation rules for the decorated Mosseri-Sadoc tiles in the
projection class of tilings . Dehn invariants related to the
stone inflation of the Mosseri-Sadoc tiles provide eigenvectors of the
inflation matrix with eigenvalues equal to and
.Comment: LaTeX file, 4(3) pages + 7 figures (FIG1.gif, FIG2.gif,... FIH7.gif)
and a style file (icqproc.sty
Differential Calculus on h-Deformed Spaces
We construct the rings of generalized differential operators on the -deformed vector space of -type. In contrast to the -deformed
vector space, where the ring of differential operators is unique up to an
isomorphism, the general ring of -deformed differential operators
is labeled by a rational function
in variables, satisfying an over-determined system of
finite-difference equations. We obtain the general solution of the system and
describe some properties of the rings
On rime Ansatz
The ice Ansatz on matrix solutions of the Yang-Baxter equation is weakened to
a condition which we call rime. Generic rime solutions of the Yang-Baxter
equation are described. We prove that the rime non-unitary (respectively,
unitary) R-matrix is equivalent to the Cremmer-Gervais (respectively, boundary
Cremmer-Gervais) solution. Generic rime classical r-matices satisfy the
(non-)homogeneous associative classical Yang-Baxter equation.Comment: 4 pages, talk given at the VII International Workshop
"Supersymmetries and Quantum Symmetries", Dubna 200
Drinfeld-Jimbo quantum Lie algebra
Quantum Lie algebras related to multi-parametric Drinfeld-Jimbo -matrices
of type are classified.Comment: 9 page
Classification of the GL(3) Quantum Matrix Groups
We define quantum matrix groups GL(3) by their coaction on appropriate
quantum planes and the requirement that the Poincare series coincides with the
classical one. It is shown that this implies the existence of a Yang-Baxter
operator. Exploiting stronger equations arising at degree four of the algebra,
we classify all quantum matrix groups GL(3). We find 26 classes of solutions,
two of which do not admit a normal ordering. The corresponding R-matrices are
given.Comment: 28 pages, Late
Classical Isomorphisms for Quantum Groups
The expressions for the --matrices for the quantum groups
SO(5) and SO(6) in terms of the --matrices for Sp(2)
and SL(4) are found, and the local isomorphisms of the corresponding
quantum groups are established.Comment: 11 page
Fusion Procedure for Cyclotomic Hecke Algebras
A complete system of primitive pairwise orthogonal idempotents for cyclotomic
Hecke algebras is constructed by consecutive evaluations of a rational function
in several variables on quantum contents of multi-tableaux. This function is a
product of two terms, one of which depends only on the shape of the
multi-tableau and is proportional to the inverse of the corresponding Schur
element
Plane partitions and their pedestal polynomials
International audienceGiven a partially ordered set S, we define, for a linear extension P of S, a multivariate polynomial, counting certain reverse partitions on S called P-pedestals. We establish a remarkable property of this polynomial: it does not depend on the choice of P. For S a Young diagram, we show that this polynomial generalizes the hook polynomial