Representation type of Hecke algebras of type $A$
HTML articles powered by AMS MathViewer
- by Karin Erdmann and Daniel K. Nakano PDF
- Trans. Amer. Math. Soc. 354 (2002), 275-285 Request permission
Abstract:
In this paper we provide a complete classification of the representation type for the blocks for the Hecke algebra of type $A$, stated in terms of combinatorical data. The computation of the complexity of Young modules is a key component in the proof of this classification result.References
- Richard Dipper and Jie Du, Trivial and alternating source modules of Hecke algebras of type $A$, Proc. London Math. Soc. (3) 66 (1993), no.Β 3, 479β506. MR 1207545, DOI 10.1112/plms/s3-66.3.479
- Richard Dipper and Gordon James, Representations of Hecke algebras of general linear groups, Proc. London Math. Soc. (3) 52 (1986), no.Β 1, 20β52. MR 812444, DOI 10.1112/plms/s3-52.1.20
- Richard Dipper and Gordon James, Blocks and idempotents of Hecke algebras of general linear groups, Proc. London Math. Soc. (3) 54 (1987), no.Β 1, 57β82. MR 872250, DOI 10.1112/plms/s3-54.1.57
- S. Donkin, The $q$-Schur algebra, London Mathematical Society Lecture Notes Series 253 (1998), Cambridge University Press.
- Yu. A. Drozd, Tame and wild matrix problems, representations and quadratic forms Institute of Mathematics, Academy of Sciences, Ukrainian SSR, Kiev 1979. A.M.S Transl. 128 (1986), 31-55.
- Karin Erdmann, Blocks of tame representation type and related algebras, Lecture Notes in Mathematics, vol. 1428, Springer-Verlag, Berlin, 1990. MR 1064107, DOI 10.1007/BFb0084003
- K. Erdmann, D.K. Nakano, Representation type of $q$-Schur algebras, to appear in Transactions of AMS.
- Gordon James, The decomposition matrices of $\textrm {GL}_n(q)$ for $n\le 10$, Proc. London Math. Soc. (3) 60 (1990), no.Β 2, 225β265. MR 1031453, DOI 10.1112/plms/s3-60.2.225
- Gordon James and Adalbert Kerber, The representation theory of the symmetric group, Encyclopedia of Mathematics and its Applications, vol. 16, Addison-Wesley Publishing Co., Reading, Mass., 1981. With a foreword by P. M. Cohn; With an introduction by Gilbert de B. Robinson. MR 644144
- Gordon James and Andrew Mathas, A $q$-analogue of the Jantzen-Schaper theorem, Proc. London Math. Soc. (3) 74 (1997), no.Β 2, 241β274. MR 1425323, DOI 10.1112/S0024611597000099
- Thomas Jost, Morita equivalence for blocks of Hecke algebras of symmetric groups, J. Algebra 194 (1997), no.Β 1, 201β223. MR 1461487, DOI 10.1006/jabr.1996.6988
- Stuart Martin, Schur algebras and representation theory, Cambridge Tracts in Mathematics, vol. 112, Cambridge University Press, Cambridge, 1993. MR 1268640, DOI 10.1017/CBO9780511470899
- J.A. de la PeΓ±a, Tame algebras: Some fundamental notions, Bielefeld preprint 095-010.
- Jeremy Rickard, The representation type of self-injective algebras, Bull. London Math. Soc. 22 (1990), no.Β 6, 540β546. MR 1099003, DOI 10.1112/blms/22.6.540
- C.M. Ringel, Tame Algebras, in Representation Theory I, (Lecture Notes in Math. 831), Springer-Verlag (1980), 137-287.
- Joanna Scopes, Cartan matrices and Morita equivalence for blocks of the symmetric groups, J. Algebra 142 (1991), no.Β 2, 441β455. MR 1127075, DOI 10.1016/0021-8693(91)90319-4
- Joanna Scopes, Symmetric group blocks of defect two, Quart. J. Math. Oxford Ser. (2) 46 (1995), no.Β 182, 201β234. MR 1333832, DOI 10.1093/qmath/46.2.201
- Carl Droms, Brigitte Servatius, and Herman Servatius, Groups assembled from free and direct products, Discrete Math. 109 (1992), no.Β 1-3, 69β75. Algebraic graph theory (Leibnitz, 1989). MR 1192371, DOI 10.1016/0012-365X(92)90279-O
Additional Information
- Karin Erdmann
- Affiliation: Mathematical Institute, Oxford University, 24-29 St. Giles, Oxford, OX1 3LB, UK
- MR Author ID: 63835
- ORCID: 0000-0002-6288-0547
- Email: erdmann@maths.ox.ac.uk
- Daniel K. Nakano
- Affiliation: Department of Mathematics, University of Georgia, Athens, Georgia 30602
- MR Author ID: 310155
- ORCID: 0000-0001-7984-0341
- Received by editor(s): September 24, 1999
- Received by editor(s) in revised form: August 18, 2000
- Published electronically: July 11, 2001
- Additional Notes: Research of the second author partially supported by NSF grant DMS-9800960
- © Copyright 2001 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 354 (2002), 275-285
- MSC (2000): Primary 16G60, 20C08
- DOI: https://doi.org/10.1090/S0002-9947-01-02848-3
- MathSciNet review: 1859276