Wydawnictwa / Banach Center Publications / Wszystkie tomy

Streszczenie

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.