To every cusp form f of weight two an AF -algebra Af (an operator algebra) is assigned. The properties of Af are studied in the case when f is a Hecke eigenform. A conjecture on the K-theory of the Bost-Connes algebra is formulated.

It is one of the aims of computational representation theory to provide tools for the explicit construction of representations of abstractly given algebras. If the algebra under consideration is given by a finite algebra presentation and the representation searched for is given by a finite module presentation, then the algorithmic tool at hand is the so-called VectorEnumerator algorithm, see Se...

We show that the center of the Iwahori–Hecke algebra of the symmetric group Sn carries a natural filtered algebra structure, and that the structure constants of the associated graded algebra are independent of n. A series of conjectures and open problems are also included.

Let (W,S) be a Coxeter system and H the associated Hecke algebra with unequal parameters. The Laurent polynomials Ms y,w and py,w for y, w ∈ W and s ∈ S play an important role in the representations of H. We study the properties of Ms y,w and py,w, the relations among them, as well as with the left, right and two-sided cells of W . In his book [5], Lusztig gave a systematic introduction to the ...

We point out that the Homfly polynomial (that is to say, Ocneanu’s trace functional) contains two polynomial-valued inner products on the Hecke algebra representation of Artin’s braid group. These bear a close connection to the Morton–Franks–Williams inequality. In these structures, the sets of positive, respectively negative permutation braids become orthonormal bases. In the second case, many...