Uno's conjecture on representation types of Hecke algebras
Uno's conjecture on representation types of Hecke algebras
Let be a field, let be an invertible element with , and let be a finite Weyl group. Let be the one-parameter Hecke algebra associated to , with quadratic relations for , and let be its Poincaré polynomial. Assume that is a splitting field of . Uno's conjecture. The algebra is of finite representation type and not semisimple if and only if is a simple root of , equivalently, if and only if does not divide . The conjecture gives a -analogue of the criterion for a group algebra of a finite Weyl group to have finite representation type. The source paper states that it proves Uno's conjecture for all Hecke algebras of classical type; its status is otherwise not resolved by the supplied text.
Progress summary
Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.
Sources & referencesView supporting material
Primary source
Susumu Ariki, “Uno's conjecture on representation types of Hecke algebras”, arXiv:math/0108176 (2003).
Solutions 0
Sign in to submit a solution.
No solutions have been posted yet.