Jucys-Murphy element and walks on modified Young graph

• Autorzy: Akihito Hora
• Języki publikacji: EN

Abstrakty

EN

Biane found out that irreducible decomposition of some representations of the symmetric group admits concentration at specific isotypic components in an appropriate large n scaling limit. This deepened the result on the limit shape of Young diagrams due to Vershik-Kerov and Logan-Shepp in a wider framework. In particular, it is remarkable that asymptotic behavior of the Littlewood-Richardson coefficients in this regime was characterized in terms of an operation in free probability of Voiculescu. These phenomena are well understood through highest order analysis in the Kerov-Olshanski algebra of polynomial functions on Young diagrams with respect to the weight degree. Taking this point of view of highest order analysis into account, we show an asymptotic formula for moments of the Jucys-Murphy element by considering an appropriate graph structure on the Young diagrams which parametrize the conjugacy classes.

Kategorie tematyczne

• 20P05: Probabilistic methods in group theory
• 20C30: Representations of finite symmetric groups
• 05E10: Combinatorial aspects of representation theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2006
• Tom: 73
• Numer: 1
• Strony: 223-235

Daty

wydano

2006

Twórcy

autor

Akihito Hora

• Faculty of Environmental Science and Technology, Okayama University, Tsushima, 700-8530 Okayama, Japan

Identyfikatory

DOI

10.4064/bc73-0-16