Multiplicative bases for the centres of the group algebra and Iwahori-Hecke algebra of the symmetric group

Andrew Francis; Lenny Jones

Multiplicative bases for the centres of the group algebra and Iwahori-Hecke algebra of the symmetric group

Andrew Francis, Lenny Jones

Research output: Chapter in Book / Conference Paper › Conference Paper › peer-review

Abstract

Let Hn be the Iwahori-Hecke algebra of the symmetric group Sn, and let Z(Hn) denote its centre. Let B = {b1,b2, ... ,bt} be a basis for Z(Hn) over R = Z[q, q- 1]. Then B is called multiplicative if, for every i and j, there exists k such that bibj = bk. In this article we prove that no multiplicative bases for Z(ZSn) and Z(Hn) when n â‰¥ 3. In addition, we prove that there exist exactly two multiplicative bases for Z(ZS2) and none for Z(H2).

Original language	English
Title of host publication	Recent Developments in Lie Algebras, Groups, and Representation Theory: 2009-2011 Southeastern Lie Theory Workshop Series: Combinatorial Lie Theory and Applications, October 9-11, 2009, North Carolina State University: Homological Methods in Representation Theory, May 22-24, 2010, University of Georgia: Finite and Algebraic Groups, June 1-4, 2011, University of Virginia
Publisher	American Mathematical Society
Pages	159-164
Number of pages	6
ISBN (Print)	9780821869178
Publication status	Published - 2012
Event	Southeastern Lie Theory Workshop: Finite and Algebraic Groups - Duration: 1 Jun 2011 → …

Conference

Conference	Southeastern Lie Theory Workshop: Finite and Algebraic Groups
Period	1/06/11 → …

Keywords

Hecke algebras

Cite this

Francis, A., & Jones, L. (2012). Multiplicative bases for the centres of the group algebra and Iwahori-Hecke algebra of the symmetric group. In Recent Developments in Lie Algebras, Groups, and Representation Theory: 2009-2011 Southeastern Lie Theory Workshop Series: Combinatorial Lie Theory and Applications, October 9-11, 2009, North Carolina State University: Homological Methods in Representation Theory, May 22-24, 2010, University of Georgia: Finite and Algebraic Groups, June 1-4, 2011, University of Virginia (pp. 159-164). American Mathematical Society.

Francis, Andrew ; Jones, Lenny. / Multiplicative bases for the centres of the group algebra and Iwahori-Hecke algebra of the symmetric group. Recent Developments in Lie Algebras, Groups, and Representation Theory: 2009-2011 Southeastern Lie Theory Workshop Series: Combinatorial Lie Theory and Applications, October 9-11, 2009, North Carolina State University: Homological Methods in Representation Theory, May 22-24, 2010, University of Georgia: Finite and Algebraic Groups, June 1-4, 2011, University of Virginia. American Mathematical Society, 2012. pp. 159-164

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title = "Multiplicative bases for the centres of the group algebra and Iwahori-Hecke algebra of the symmetric group",

abstract = "Let Hn be the Iwahori-Hecke algebra of the symmetric group Sn, and let Z(Hn) denote its centre. Let B = {b1,b2, ... ,bt} be a basis for Z(Hn) over R = Z[q, q- 1]. Then B is called multiplicative if, for every i and j, there exists k such that bibj = bk. In this article we prove that no multiplicative bases for Z(ZSn) and Z(Hn) when n {\^a}‰¥ 3. In addition, we prove that there exist exactly two multiplicative bases for Z(ZS2) and none for Z(H2).",

keywords = "Hecke algebras",

author = "Andrew Francis and Lenny Jones",

year = "2012",

language = "English",

isbn = "9780821869178",

pages = "159--164",

booktitle = "Recent Developments in Lie Algebras, Groups, and Representation Theory: 2009-2011 Southeastern Lie Theory Workshop Series: Combinatorial Lie Theory and Applications, October 9-11, 2009, North Carolina State University: Homological Methods in Representation Theory, May 22-24, 2010, University of Georgia: Finite and Algebraic Groups, June 1-4, 2011, University of Virginia",

publisher = "American Mathematical Society",

note = "Southeastern Lie Theory Workshop: Finite and Algebraic Groups ; Conference date: 01-06-2011",

}

Francis, A & Jones, L 2012, Multiplicative bases for the centres of the group algebra and Iwahori-Hecke algebra of the symmetric group. in Recent Developments in Lie Algebras, Groups, and Representation Theory: 2009-2011 Southeastern Lie Theory Workshop Series: Combinatorial Lie Theory and Applications, October 9-11, 2009, North Carolina State University: Homological Methods in Representation Theory, May 22-24, 2010, University of Georgia: Finite and Algebraic Groups, June 1-4, 2011, University of Virginia. American Mathematical Society, pp. 159-164, Southeastern Lie Theory Workshop: Finite and Algebraic Groups, 1/06/11.

Multiplicative bases for the centres of the group algebra and Iwahori-Hecke algebra of the symmetric group. / Francis, Andrew; Jones, Lenny.
Recent Developments in Lie Algebras, Groups, and Representation Theory: 2009-2011 Southeastern Lie Theory Workshop Series: Combinatorial Lie Theory and Applications, October 9-11, 2009, North Carolina State University: Homological Methods in Representation Theory, May 22-24, 2010, University of Georgia: Finite and Algebraic Groups, June 1-4, 2011, University of Virginia. American Mathematical Society, 2012. p. 159-164.

Research output: Chapter in Book / Conference Paper › Conference Paper › peer-review

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T1 - Multiplicative bases for the centres of the group algebra and Iwahori-Hecke algebra of the symmetric group

AU - Francis, Andrew

AU - Jones, Lenny

PY - 2012

Y1 - 2012

N2 - Let Hn be the Iwahori-Hecke algebra of the symmetric group Sn, and let Z(Hn) denote its centre. Let B = {b1,b2, ... ,bt} be a basis for Z(Hn) over R = Z[q, q- 1]. Then B is called multiplicative if, for every i and j, there exists k such that bibj = bk. In this article we prove that no multiplicative bases for Z(ZSn) and Z(Hn) when n â‰¥ 3. In addition, we prove that there exist exactly two multiplicative bases for Z(ZS2) and none for Z(H2).

AB - Let Hn be the Iwahori-Hecke algebra of the symmetric group Sn, and let Z(Hn) denote its centre. Let B = {b1,b2, ... ,bt} be a basis for Z(Hn) over R = Z[q, q- 1]. Then B is called multiplicative if, for every i and j, there exists k such that bibj = bk. In this article we prove that no multiplicative bases for Z(ZSn) and Z(Hn) when n â‰¥ 3. In addition, we prove that there exist exactly two multiplicative bases for Z(ZS2) and none for Z(H2).

KW - Hecke algebras

UR - http://handle.uws.edu.au:8081/1959.7/520803

M3 - Conference Paper

SN - 9780821869178

SP - 159

EP - 164

BT - Recent Developments in Lie Algebras, Groups, and Representation Theory: 2009-2011 Southeastern Lie Theory Workshop Series: Combinatorial Lie Theory and Applications, October 9-11, 2009, North Carolina State University: Homological Methods in Representation Theory, May 22-24, 2010, University of Georgia: Finite and Algebraic Groups, June 1-4, 2011, University of Virginia

PB - American Mathematical Society

T2 - Southeastern Lie Theory Workshop: Finite and Algebraic Groups

Y2 - 1 June 2011

ER -

Francis A, Jones L. Multiplicative bases for the centres of the group algebra and Iwahori-Hecke algebra of the symmetric group. In Recent Developments in Lie Algebras, Groups, and Representation Theory: 2009-2011 Southeastern Lie Theory Workshop Series: Combinatorial Lie Theory and Applications, October 9-11, 2009, North Carolina State University: Homological Methods in Representation Theory, May 22-24, 2010, University of Georgia: Finite and Algebraic Groups, June 1-4, 2011, University of Virginia. American Mathematical Society. 2012. p. 159-164

Multiplicative bases for the centres of the group algebra and Iwahori-Hecke algebra of the symmetric group

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