Wreath Product Action on Generalized Boolean Algebras

Mishra, Ashish; Srinivasan, Murali K.

doi:10.37236/4831

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Theorem 610 Consider the Basis ∪1

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“…and Tolli [1,2] (also see [8]). We consider multiplicity free S n , G n -actions and explicitly write down the GZ-vectors (in the S n case) and the GZ-subspaces (in the G n case) and also identify the irreducibles which occur.…”

Section: Theorem 610 Consider the Basis ∪mentioning

confidence: 99%

On the representation theory of $G\sim S_n$

Mishra,

Srinivasan

2015

Preprint

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In the Vershik-Okounkov approach to the complex irreducible representations of S n and G ∼ S n we parametrize the irreducible representations and their bases by spectral objects rather than combinatorial objects and then, at the end, give a bijection between the spectral and combinatorial objects. The fundamental ideas are similar in both cases but there are additional technicalities involved in the G ∼ S n case. This was carried out by Pushkarev.The present work gives a fully detailed exposition of Pushkarev's theory. For the most part we follow the original but our definition of a Gelfand-Tsetlin subspace, based on a multiplicity free chain of subgroups, is slightly different and leads to a more natural development of the theory. We also work out in detail an example, the generalized Johnson scheme, from this viewpoint.

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Section: Theorem 610 Consider the Basis ∪mentioning

confidence: 99%