Dilute Birman-Wenzl-Murakami algebra and Dn+1(2) models

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“Dilute” Birman–Wenzl–Murakami Algebra

Explicit expressions for three series of R matrices which are related to a “dilute” generalisation of the Birman–Wenzl–Murakami algebra are presented. Of those, one series is equivalent to the quantum R matrices of the D (2) n+1 generalised Toda systems whereas the remaining two series appear to be new. A “dilute” generalisation of the Birman–Wenzl–Murakami (BWM) algebra [1, 2] has recently bee...

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Birman-Wenzl-Murakami Algebra and Logarithmic Superconformal Minimal Models

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Incompressible representations of the Birman-Wenzl-Murakami algebra

We construct a representation of the Birman-Wenzl-Murakami algebra acting on a space of polynomials in n variables vanishing when three points coincide. These polynomials are closely related to the Pfaffian state of the Quantum Hall Effect and to the components the transfer matrix eigenvector of a O(n) crossing loop model.

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Cellularity of Cyclotomic Birman–wenzl–murakami Algebras

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THE BIRMAN–MURAKAMI–WENZL ALGEBRAS OF TYPE Dn

The Birman–Murakami–Wenzl algebra (BMW algebra) of type Dn is shown to be semisimple and free over Z[δ±1, l±1]/(m(1− δ)− (l− l−1)) of rank (2n + 1)n!! − (2n−1 + 1)n!, where n!! = 1 · 3 · · · (2n − 1). We also show it is a cellular algebra over suitable rings. The Brauer algebra of type Dn is a homomorphic ring image and is also semisimple and free of the same rank, but over the ring Z[δ±1]. A r...

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ژورنال

عنوان ژورنال: Journal of Physics A: Mathematical and General

سال: 1994

ISSN: 0305-4470,1361-6447

DOI: 10.1088/0305-4470/27/17/022