Murphy Operators and the Centre of the Iwahori-Hecke Algebras of Type A
Andrew Mathas
DOI: 10.1023/A:1018604404327
Abstract
In this paper we introduce a family of polynomials indexed by pairs of partitions and show that if these polynomials are self-orthogonal then the centre of the Iwahori-Hecke algebra of the symmetric group is precisely the set of symmetric polynomials in the Murphy operators.
Pages: 295–313
Keywords: Hecke algebra; murphy operator; symmetric group
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References
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2. R. Dipper and G. James, “Blocks and idempotents of Hecke algebras of general linear groups,” Proc. London Math. Soc. 54 (1987), 57-82.
3. G.D. James and A. Mathas, “A q-analogue of the Jantzen-Schaper theorem,” Proc. London Math. Soc. 74 (3) (1997), 241-274.
4. G.E. Murphy, “The idempotents of the symmetric group and Nakayama's conjecture,” J. Algebra 81 (1983), 258-265.
5. M. Sch\ddot onert et al., “Gap: groups, algorithms, and programming,” Lehrstuhl D f\ddot ur Mathematik, RWTH Aachen, 3.4.4 edition, 1997.