907 research outputs found
Bethe subalgebras in affine Birman--Murakami--Wenzl algebras and flat connections for q-KZ equations
Commutative sets of Jucys-Murphyelements for affine braid groups of
types were defined. Construction of
-matrix representations of the affine braid group of type and its
distinguish commutative subgroup generated by the -type Jucys--Murphy
elements are given. We describe a general method to produce flat connections
for the two-boundary quantum Knizhnik-Zamolodchikov equations as necessary
conditions for Sklyanin's type transfer matrix associated with the two-boundary
multicomponent Zamolodchikov algebra to be invariant under the action of the
-type Jucys--Murphy elements. We specify our general construction to
the case of the Birman--Murakami--Wenzl algebras. As an application we suggest
a baxterization of the Dunkl--Cherednik elements in the double affine
Hecke algebra of type
On quantum matrix algebras satisfying the Cayley-Hamilton-Newton identities
The Cayley-Hamilton-Newton identities which generalize both the
characteristic identity and the Newton relations have been recently obtained
for the algebras of the RTT-type. We extend this result to a wider class of
algebras M(R,F) defined by a pair of compatible solutions of the Yang-Baxter
equation. This class includes the RTT-algebras as well as the Reflection
equation algebras
On R-matrix representations of Birman-Murakami-Wenzl algebras
We show that to every local representation of the Birman-Murakami-Wenzl
algebra defined by a skew-invertible R-matrix one can
associate pairings and , where V is the
representation space. Further, we investigate conditions under which the
corresponding quantum group is of SO or Sp type.Comment: 9 page
Modified Affine Hecke Algebras and Drinfeldians of Type A
We introduce a modified affine Hecke algebra \h{H}^{+}_{q\eta}({l})
(\h{H}_{q\eta}({l})) which depends on two deformation parameters and
. When the parameter is equal to zero the algebra
\h{H}_{q\eta=0}(l) coincides with the usual affine Hecke algebra
\h{H}_{q}(l) of type , if the parameter q goes to 1 the algebra
\h{H}^{+}_{q=1\eta}(l) is isomorphic to the degenerate affine Hecke algebra
\Lm_{\eta}(l) introduced by Drinfeld. We construct a functor from a category
of representations of into a category of representations of
Drinfeldian which has been introduced by the first author.Comment: 11 pages, LATEX. Contribution to Proceedings "Quantum Theory and
Symmetries" (Goslar, July 18-22, 1999) (World Scientific, 2000
Modified Braid Equations for SO_q (3) and noncommutative spaces
General solutions of the equation with a maximal number of free
parameters in the specrtal decomposition of vector
matrices are implemented to construct modified braid equations (MBE). These
matrices conserve the given, standard, group relations of the nine elements of
T, but are not constrained to satisfy the standard braid equation (BE). Apart
from q and a normalisation factor our contains two free parameters,
instead of only one such parameter for deformed unitary algebras studied in a
previous paper [1] where the nonzero right hand side of the had a linear
term proprotional to . In the present case
the r.h.s. is, in general, nonliear. Several particular solutions are given
(Sec.2) and the general structure is analysed (App.A). Our formulation of the
problem in terms of projectors yield also two new solutions of standard
(nonmodified) braid equation (Sec.2) which are further discussed (App.B). The
noncommutative 3-spaces obtained by implementing such generalized
matrices are studied (Sec.3). The role of coboundary matrices (not
satisfying the standard BE) is explored. The MBE and Baxterization are
presented as complementary facets of the same basic construction, namely, the
general solution of equation (Sec.4). A new solution is presented
in this context. As a simple but remarkable particular case a nontrivial
solution of BE is obtained (App.B) for q=1. This solution has no free parameter
and is not obtainable by twisting the identity matrix. In the concluding
remarks (Sec.5), among other points, generalisation of our results to
is discussed.Comment: 18 pages, no figure
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