Geetha, T. ; Prasad, Amritanshu (2018) Comparison of Gelfand-Tsetlin Bases for Alternating and Symmetric Groups Algebras and Representation Theory, 21 (1). pp. 131-143. ISSN 1386-923X
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Official URL: http://doi.org/10.1007/s10468-017-9706-z
Related URL: http://dx.doi.org/10.1007/s10468-017-9706-z
Abstract
Young’s orthogonal basis is a classical basis for an irreducible representation of a symmetric group. This basis happens to be a Gelfand-Tsetlin basis for the chain of symmetric groups. It is well-known that the chain of alternating groups, just like the chain of symmetric groups, has multiplicity-free restrictions for irreducible representations. Therefore each irreducible representation of an alternating group also admits Gelfand-Tsetlin bases. Moreover, each such representation is either the restriction of, or a subrepresentation of, the restriction of an irreducible representation of a symmetric group. In this article, we describe a recursive algorithm to write down the expansion of each Gelfand-Tsetlin basis vector for an irreducible representation of an alternating group in terms of Young’s orthogonal basis of the ambient representation of the symmetric group. This algorithm is implemented with the Sage Mathematical Software.
Item Type: | Article |
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Source: | Copyright of this article belongs to Springer Nature Switzerland AG. |
ID Code: | 121494 |
Deposited On: | 17 Jul 2021 08:09 |
Last Modified: | 17 Jul 2021 08:09 |
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