Coherent systems of probability measures on graphs for representations of free Frobenius towers
Guardado en:
| Publicado en: | arXiv.org (Oct 26, 2018), p. n/a |
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| Autor principal: | |
| Publicado: |
Cornell University Library, arXiv.org
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| Materias: | |
| Acceso en línea: | Citation/Abstract Full text outside of ProQuest |
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| Resumen: | First formally defined by Borodin and Olshanski, a coherent system on a graded graph is a sequence of probability measures which respect the action of certain down/up transition functions between graded components. In one common example of such a construction, each measure is the Plancherel measure for the symmetric group \(S_{n}\) and the down transition function is induced from the inclusions \(S_{n} \hookrightarrow S_{n+1}\). In this paper we generalize the above framework to the case where \(\{A_n\}_{n \geq 0}\) is any free Frobenius tower and \(A_n\) is no longer assumed to be semisimple. In particular, we describe two coherent systems on graded graphs defined by the representation theory of \(\{A_n\}_{n \geq 0}\) and connect one of these systems to a family of central elements of \(\{A_n\}_{n \geq 0}\). When the algebras \(\{A_n\}_{n \geq 0}\) are not semisimple, the resulting coherent systems reflect the duality between simple \(A_n\)-modules and indecomposable projective \(A_n\)-modules. |
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| ISSN: | 2331-8422 |
| Fuente: | Engineering Database |