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arXiv · 1409.0216

Nonstandard representations of type C affine Hecke algebra from K-operators

Kohei Motegi
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Abstract

We construct nonstandard finite-dimensional representations of type C affine Hecke algebra from the viewpoint of quantum integrable models. There exists two classes of nonstandard solutions to the Yang-Baxter equation called the Cremmer-Gervais and Jordanian R-matrices. These R-matrices also satisfy the Hecke-relation, thus can be used to construct nonstandard finite-dimensional representations of type A affine Hecke algebra. We construct the corresponding nonstandard representations for type C affine Hecke algebra by explicitly constructing solutions to the reflection equation under the Hecke relation. We achieve this by taking the finite-dimensional representations and deBaxterizing the K-operators acting on the infinite-dimensional function space, taking advantage of the fact that the Cremmer-Gervais and Jordanian R-matrices can be obtained from the R-operator.

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Kohei Motegi. 2015-07-05. Nonstandard representations of type C affine Hecke algebra from K-operators. https://doi.org/10.1007/s11005-015-0772-z

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