Intertwining spaces associated with q-analogues of the Young symmetrizers in the Hecke algebra

• Autorzy: Gérard Duchamp , Sungsoon Kim
• Języki publikacji: EN FR

Abstrakty

EN

Abstract. Let H be the Hecke algebra of the symmetric group. With each subset S ⊂ [1,n-1], we associate two idempotents $□_S$ and $∇_S$ which are q-deformations of the symmetrizer and antisymmetrizer relative to the Young subgroup ${\goth S}_{I_S}$ generated by the simple transpositions ${(i,i+1)}_{i ∈ S}$. We give here explicit bases for the intertwining space $□_{S_1}H ∇_{S_2}$, indexed by the double classes ${\goth S}_{I_{S_1}}\{\goth S}_n/{\goth S}_{I_{S_2}}$. We also compute bases and characters of the right ideals {\goth I}(I,J)= □_{S_1}H ∇_{S_2}H.

FR

Résumé. Soit H, l'algèbre de Hecke du groupe symétrique. À chaque sous ensemble S ⊂ [1,n-1], on associe deux idempotents $□_S$ et $∇_S$ qui sont les q-déformations des symétriseur et antisymétriseur du sous groupe de Young ${\goth S}_{I_S}$ engendré par les transpositions simples ${(i,i+1)}_{i ∈ S}$. Nous donnons ici des bases explicites pour le sous espace d'entrelacement $□_{S_1}H ∇_{S_2}$, indexées par les doubles classes ${\goth S}_{I_{S_1}}\{\goth S}_n/{\goth S}_{I_{S_2}}$. Nous calculons également des bases et les caractères des idéaux {\goth I}(I,J)= □_{S_1}H ∇_{S_2}H.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1996
• Tom: 36
• Numer: 1
• Strony: 61-70

Daty

wydano

1996

Twórcy

autor

Gérard Duchamp

• L.I.R., Université de Rouen, Place E. Blondel, B.P. 118, 76134 Mont-Saint-Aignan Cedex, France

autor

Sungsoon Kim

• L.I.T.P., Université Paris 7, 2 place Jussieu, 75251 Paris Cedex 05, France

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