On the complexity of multiplication in the Iwahori–Hecke algebra of the symmetric group. (May 2017)

• Record Type: Journal Article
• Authors: Niemeyer, Alice C.; Pfeiffer, Götz; Praeger, Cheryl E.
• Is Part Of: Journal of symbolic computation. Volume 80:Part 3(2017)
• Page Start: 817
• Page End: 832
• Publication Date: 2017-05
• Subjects: 20C08 -- 20F55 -- 20B40; Iwahori–Hecke algebra -- Finite Coxeter group -- Symmetric group -- Complexity; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2016.09.001
• Languages: English
• ISSNs: 0747-7171

Abstract

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 ) .