On the complexity of multiplication in the Iwahori–Hecke algebra of the symmetric group

Alice C. Niemeyer; Götz Pfeiffer; Cheryl E. Praeger

doi:10.1016/j.jsc.2016.09.001

On the complexity of multiplication in the Iwahori–Hecke algebra of the symmetric group

Alice C. Niemeyer, Götz Pfeiffer, Cheryl E. Praeger

Research output: Contribution to journal › Article › peer-review

Abstract

We present new efficient data structures for elements of Coxeter groups of type A_m and their associated Iwahori–Hecke algebras H(A_m). Usually, elements of H(A_m) are represented as simple coefficient list of length M=(m+1)! with respect to the standard basis, indexed by the elements of the Coxeter group. In the new data structure, elements of H(A_m) are represented as nested coefficient lists. While the cost of addition is the same in both data structures, the new data structure leads to a huge improvement in the cost of multiplication in H(A_m).

Original language	English
Pages (from-to)	817-832
Number of pages	16
Journal	Journal of Symbolic Computation
Volume	80
DOIs	https://doi.org/10.1016/j.jsc.2016.09.001
Publication status	Published - 1 May 2017

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title = "On the complexity of multiplication in the Iwahori–Hecke algebra of the symmetric group",

abstract = "We present new efficient data structures for elements of Coxeter groups of type Am and their associated Iwahori–Hecke algebras H(Am). Usually, elements of H(Am) are represented as simple coefficient list of length M=(m+1)! with respect to the standard basis, indexed by the elements of the Coxeter group. In the new data structure, elements of H(Am) are represented as nested coefficient lists. While the cost of addition is the same in both data structures, the new data structure leads to a huge improvement in the cost of multiplication in H(Am).",

keywords = "Complexity, Finite Coxeter group, Iwahori–Hecke algebra, Symmetric group",

author = "Niemeyer, {Alice C.} and G{\"o}tz Pfeiffer and Praeger, {Cheryl E.}",

year = "2017",

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doi = "10.1016/j.jsc.2016.09.001",

language = "English",

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T1 - On the complexity of multiplication in the Iwahori–Hecke algebra of the symmetric group

AU - Niemeyer, Alice C.

AU - Pfeiffer, Götz

AU - Praeger, Cheryl E.

PY - 2017/5/1

Y1 - 2017/5/1

N2 - We present new efficient data structures for elements of Coxeter groups of type Am and their associated Iwahori–Hecke algebras H(Am). Usually, elements of H(Am) are represented as simple coefficient list of length M=(m+1)! with respect to the standard basis, indexed by the elements of the Coxeter group. In the new data structure, elements of H(Am) are represented as nested coefficient lists. While the cost of addition is the same in both data structures, the new data structure leads to a huge improvement in the cost of multiplication in H(Am).

AB - We present new efficient data structures for elements of Coxeter groups of type Am and their associated Iwahori–Hecke algebras H(Am). Usually, elements of H(Am) are represented as simple coefficient list of length M=(m+1)! with respect to the standard basis, indexed by the elements of the Coxeter group. In the new data structure, elements of H(Am) are represented as nested coefficient lists. While the cost of addition is the same in both data structures, the new data structure leads to a huge improvement in the cost of multiplication in H(Am).

KW - Complexity

KW - Finite Coxeter group

KW - Iwahori–Hecke algebra

KW - Symmetric group

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DO - 10.1016/j.jsc.2016.09.001

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SN - 0747-7171

VL - 80

SP - 817

EP - 832

JO - Journal of Symbolic Computation

JF - Journal of Symbolic Computation

ER -

On the complexity of multiplication in the Iwahori–Hecke algebra of the symmetric group

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