Automatic Construction of Explicit R Matrices for the One-Parameter Families of Irreducible Typical Highest Weight (0|α) Representations of U_q[gl(m|n)]

Details Automatic Construction of Explicit R Matrices for the One-Parameter Families of Irreducible Typical Highest Weight (0|α) Representations of U_q[gl(m|n)] Automatic Construction of Explicit R Matrices for the One-Parameter Families of Irreducible Typical Highest Weight (0|α) Representations of U_q[gl(m|n)]

2001-01-04

arxiv.org/abs/math/0101027v1

Computer Physics Communications 145(2):(15 May 2002) 205-255

Mathematics

Quantum Algebra

65 pages, 6 tables. David De Wit: <http://www.kurims.kyoto-u.ac.jp/~ddw>

Scientific paper

10.1016/S0010-4655(01)00463-5

We detail the automatic construction of R matrices corresponding to (the tensor products of) the (0|\alpha) families of highest-weight representations of the quantum superalgebras U_q[gl(m|n)]. These representations are irreducible, contain a free complex parameter \alpha, and are 2^{mn} dimensional. Our R matrices are actually (sparse) rank 4 tensors, containing a total of 2^{4mn} components, each of which is in general an algebraic expression in the two complex variables q and \alpha. Although the constructions are straightforward, we describe them in full here, to fill a perceived gap in the literature. As the algorithms are generally impracticable for manual calculation, we have implemented the entire process in Mathematica; illustrating our results with U_q[gl(3|1)].

Affiliated with

Also associated with

No associations

Rating

Automatic Construction of Explicit R Matrices for the One-Parameter Families of Irreducible Typical Highest Weight (0|α) Representations of U_q[gl(m|n)] does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Automatic Construction of Explicit R Matrices for the One-Parameter Families of Irreducible Typical Highest Weight (0|α) Representations of U_q[gl(m|n)], we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Automatic Construction of Explicit R Matrices for the One-Parameter Families of Irreducible Typical Highest Weight (0|α) Representations of U_q[gl(m|n)] will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-151534