ON THE DECOMPOSITION NUMBERS OF THE HECKE ALGEBRA OF TYPE Dn WHEN n IS EVEN
نویسنده
چکیده
Let n ≥ 4 be an even integer. Let K be a field with charK 6= 2 and q an invertible element in K such that Qn−1 i=1 (1+q ) 6= 0. In this paper, we study the decomposition numbers over K of the Iwahori–Hecke algebra Hq(Dn) of type Dn. We obtain some equalities which relate its decomposition numbers with certain Schur elements and the decomposition numbers of various Iwahori–Hecke algebras of type A with the same parameter q. When charK = 0, this completely determine all of its decomposition numbers. The main tools we used are the Morita equivalence theorem established in [19] and certain twining character formulae of Weyl modules over a tensor product of two q-Schur algebras.
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