查看更多>>摘要：In 2007, B. Hartwig and Terwilliger found a presentation for the three-point sl(2) loop algebra in terms of generators and relations. To obtain this presentation, they defined a Lie algebra boxed times by generators and relations and established an isomorphism from boxed times to three-point sl(2) loop algebra. Essentially, boxed times has six generators which can be naturally identified with the six edges of the tetrahedron. In fact, each face of the tetrahedron has three surrounding edges which generate a subalgebra of boxed times that is isomorphic to sl(2). It is interesting to know whether a direct sum of finitely many copies of sl(2) (e.g., special orthogonal algebra so(4)) captures the bracket relations of the generators of boxed times. Here, we show that there exists a Lie algebra homomorphism phi : boxed times -> so(4) which can be extended to a homomorphism phi : boxed times -> L where L is a direct sum of finitely many copies of sl(2). We construct a finite-dimensional so(4)-module which is viewed as a boxed times-module via the homomorphism phi. We show how this so(4)-module is related to Krawtchouk polynomials. This paper is inspired by and is an extension of the work of Nomura and Terwilliger (2012) [19]. (c) 2021 Elsevier Inc. All rights reserved.
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