Representations of Hecke Algebras of Type Dn

Modular representations of Hecke algebras of type G(p,p,n)

“…This is the main reason that why in this case we could give a classification of all the simple H p,p,n -modules. In the special case where p = 2, we recover the results in [28] and [22] for the Hecke algebra of type D n satisfying "separation condition". In the case that "separation condition" does not hold, a complete classification of all the simple modules for the Hecke algebra of type D n is obtained in [23], and in [17] by a different method.…”

“…In these work the Specht modules, which are defined as "cell modules" via cellular basis, play an important role. The modular representations of the Hecke algebra H 2,2,n (i.e., the Hecke algebra of type D n ) were studied in [22,23,28] and [17]. However, for arbitrary p, r, n with p | r, the modular representations of the Hecke algebra H r,p,n is less studied.…”

A note on the representation theory of the Hecke algebra of type F4

“…Note that for the choices of / and e given below, e = ke for some k e K, k =£ 0, and fHe was proved to be 1-dimensional as a vector space over K (compare Corollary 3.2 and the case m = 11). 50 C. A. PALLIKAROS y>i)H = EH for some idempotent e. Thus, considering x 6 He as a vector space over K, we expect to be able to construct a 16-dimensional representation of H which, upon specializing q, Q to 1 has character Xis-…”

“…Now * 6 //(W,) is 3-dimensional and yi)H(W 2 ) is 2-dimensional as vector spaces over K, so it is not necessarily true that either of x\ = kx 6 or y\ = ky g holds. However, if H is semisimple,…”

Cohomology of Hecke algebras

“…We set f n (q) = 2 n−1 i=1 (1 + q i ). The next theorem is implicit in Theorems 3.6 and 3.7 of Pallikaros [11] and is made explicit in Hu [9]. where A(n/2) is an explicitly described algebra.…”