Abstract
We define an analog of Zelevinsky involution on degenerate affine Hecke—Clifford algebras and give an algorithm to compute its action on irreducible completely splittable representations over an algebraically closed field of characteristic not equal to 2 via placed skew shifted Young diagrams.
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Acknowledgements
The second author is supported by NSFC (Nos. 12071026, 12122101) and the paper was partially written up during her visit to University of Virginia, from which she gratefully acknowledges the support and excellent working environment.
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He, Z., Wan, J. Zelevinsky Involution and Degenerate Affine Hecke—Clifford Algebras. Front. Math 18, 47–63 (2023). https://doi.org/10.1007/s11464-021-0241-1
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DOI: https://doi.org/10.1007/s11464-021-0241-1
Keywords
- Degenerate affine Hecke—Clifford algebra
- Zelevinsky involution
- completely splittable representation
- skew Young diagram