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

Volume 36 / 1996

Gérard Duchamp, Sungsoon Kim Banach Center Publications 36 (1996), 61-70 DOI: 10.4064/-36-1-61-70


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.


  • Gérard Duchamp
  • Sungsoon Kim

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