Centralizer Algebras and Degenerate Affine Hecke Algebras

REFERENCES

• Alperin , J. L. ( 1987 ). Weights for finite groups . Proc. Symp. Pure Math. 47 : 369 – 379 .
   Google Scholar
• Alperin , J. L. ( 2008 ). On the centre of a Hecke algebra . J. Algebra 319 : 777 – 778 .
   Web of Science ®Google Scholar
• Bernstein , I. N. , Zelevinsky A. V. (1977). Induced representations of reductive p-adic groups I. Ann. Sci. École Norm. Sup. 10:441–472.
   Web of Science ®Google Scholar
• Bessenrodt , C. ( 1998 ). On hooks of Young diagrams . Ann. Comb. 2 : 103 – 110 .
   Google Scholar
• Brundan , J. ( 2008 ). Centres of degenerate cyclotomic Hecke algebras and parabolic category 𝒪 . Represent. Theory 12 : 236 – 259 .
   Google Scholar
• Ceccherini-Silberstein , T. , Scarabotti , F. , Tolli , F. ( 2010 ). Representation Theory of the Symmetric Groups: The Okounkov-Vershik Approach, Character Formulas, and Partition Algebras. Cambridge Stud. Adv. Math. Vol. 121. Cambridge Univ. Press .
   Google Scholar
• Danz , S. , Ellers , H. , Murray , J. ( 2013 ). The centralizer of a subgroup in a group algebra . Proc. Edinburgh Math. Soc. 56 : 49 – 56 .
   Web of Science ®Google Scholar
• Ellers , H. ( 1994 ). The centralizer of a subgroup in a group algebra. Alperin's conjecture . J. Reine Angnew. Math. 468 : 1 – 48 .
   Google Scholar
• Ellers , H. ( 2000 ). Searching for more general weight conjectures, using the Symmetric group as an example . J. Algebra 225 : 602 – 629 .
   Web of Science ®Google Scholar
• Ellers , H. , Murray , J. ( 2004 ). Block theory, branching rules, and centralizer algebras . J. Algebra 276 : 236 – 258 .
   Web of Science ®Google Scholar
• Feit , W. ( 1982 ). The Representation Theory of Finite Groups . Amsterdam-New York : North-Holland .
   Google Scholar
• James , G. D. ( 1978 ). The Representation Theory of the Symmetric Groups . Lecture Notes in Math . Vol. 682 . Berlin : Springer-Verlag .
   Google Scholar
• James , G. D. ( 1978 II). Some combinatorial results involving Young diagrams . Math. Proc. Camb. Philos. Soc. 83 : 1 – 10 .
   Web of Science ®Google Scholar
• James , G. D. , Kerber , A. ( 1985 ). The Representation Theory of the Symmetric Group. Encyclopedia Math. Applic. Vol. 16. Cambridge Univ. Press .
   Google Scholar
• Kleshchev , A. S. ( 1995 ). Branching rules for modular representations of symmetric groups I . J. Algebra 178 : 493 – 511 .
   Web of Science ®Google Scholar
• Kleshchev , A. S. ( 2005 ). Linear and Projective Representations of Symmetric Groups . Cambridge : Cambridge University Press .
   Google Scholar
• Murphy , G. E. ( 1981 ). A new construction of Young's seminormal representation of the symmetric groups . J. Algebra 69 : 287 – 297 .
   Web of Science ®Google Scholar
• Nagao , H. , Tsushima , Y. ( 1987 ). Representations of Finite Groups . Boston : Academic Press .
   Google Scholar
• Okounkov , A. , Vershik , A. ( 1996 ). A new approach to representation theory of symmetric groups . Selecta Math. New Series 2 , 4 : 581 – 605 .
   Google Scholar
• Robinson , G. R. ( 1994 ). Some remarks on Hecke algebras . J. Algebra 163 : 806 – 812 .
   Web of Science ®Google Scholar
• Strahov , E. ( 2007 ). Generalized characters of the symmetric groups . Adv. Math. 212 : 109 – 142 .
   Web of Science ®Google Scholar
• Vazirani , M. ( 1999 ). Irreducible Modules over the Affine Hecke Algebra: A Strong Multiplicity One Result. Ph.D. Thesis, University of California at Berkeley .
   Google Scholar
• Communicated by A. Turull.
   Google Scholar