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REPRESENTATIONS OF TWISTED YANGIANS OF TYPES B, C, D: II

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Abstract

We continue the study of finite-dimensional irreducible representations of twisted Yangians associated to symmetric pairs of types B, C and D, with focus on those of types BI, CII and DI. After establishing that, for all twisted Yangians of these types, the highest weight of such a module necessarily satisfies a certain set of relations, we classify the finite-dimensional irreducible representations of twisted Yangians for the pairs (\( \mathfrak{s}{\mathfrak{o}}_N \), \( \mathfrak{s}{\mathfrak{o}}_{N-2} \) ⊕ \( \mathfrak{s}{\mathfrak{o}}_2 \)) and (\( \mathfrak{s}{\mathfrak{o}}_{2n+1} \), \( \mathfrak{s}{\mathfrak{o}}_{2n} \)).

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Authors and Affiliations

  1. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Canada

    N. GUAY & C. WENDLANDT

  2. Department of Mathematics, University of York, York, YO10 5DD, UK

    V. REGELSKIS

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  1. N. GUAY
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  2. V. REGELSKIS
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  3. C. WENDLANDT
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Correspondence to N. GUAY.

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Supported by a Discovery Grant of the Natural Sciences and Engineering Research Council of Canada.

Supported in part by the Engineering and Physical Sciences Research Council of the United Kingdom, grant number EP/K031805/1. V.R. thanks the University of Alberta for its hospitality.

Supported by an Alexander Graham Bell Canada Graduate Scholarship (Doctoral Program) of the Natural Sciences and Engineering Research Council of Canada.

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GUAY, N., REGELSKIS, V. & WENDLANDT, C. REPRESENTATIONS OF TWISTED YANGIANS OF TYPES B, C, D: II. Transformation Groups 24, 1015–1066 (2019). https://doi.org/10.1007/s00031-019-09514-x

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