The grant was used to support two visits of Prof Jean-Yves Thibon (Université de Marne-la-Vallée, France) to the Univestity of York, in September 1999 and in May 2000. The aim of the project was to develop further the representation theory of the Hecke algebra Hn of the group GLn over a p-adic field, relative to the Iwahori subgroup. We found an explicit irreducibility criterion for a wide class of induced representations of the algebra Hn . Representations of this class are parametrised by sequences of pairs consisting of a Young diagram and a complex number, the total number of boxes in these diagrams being n . In the particular case when each of these Young diagrams consists of one row only, such a criterion was given by Zelevinsky in 1980. He used the representation theory of the p-adic group GLn itself. We employed the canonical basis, due to Kashiwara and Lusztig, in the quantum coordinate ring of the complex group of triangular unipotent matrices. Our results are available on the e-print archive Mathematics, see
EPSRC Grant and Duration: £ 2380 over 12 months from 13.9.1997, reference GR/M67155
For further information please contact: Dr ML Nazarov, Department of Mathematics, University of York, York YO10 5DD, England; maxim.nazarov@york.ac.uk