A note on bideterminants for Schur superalgebras

Frantisek Marko; Alexandr N. Zubkov

doi:10.1016/j.jpaa.2011.02.003

A note on bideterminants for Schur superalgebras

Frantisek Marko
, Alexandr N. Zubkov

Penn State Hazleton

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

3 Scopus citations

Abstract

Let S(m|n,r)_Z be a Z-form of a Schur superalgebra S(m|n,r) generated by elements ξ_i,j. We solve a problem of Muir and describe a Z-form of a simple S(m|n,r)-module Dλ,Q over the field Q of rational numbers, under the action of S(m|n,r)Z. This Z-form is the Z-span of modified bideterminants [Tℓ:Ti] defined in this work. We also prove that each [Tℓ:Ti] is a Z-linear combination of modified bideterminants corresponding to (m|n)-semistandard tableaux T_i.

Original language	English (US)
Pages (from-to)	2223-2230
Number of pages	8
Journal	Journal of Pure and Applied Algebra
Volume	215
Issue number	9
DOIs	https://doi.org/10.1016/j.jpaa.2011.02.003
State	Published - Sep 2011

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

Access to Document

10.1016/j.jpaa.2011.02.003

Cite this

@article{e7b74682110f424cba3122f5f8c69da0,

title = "A note on bideterminants for Schur superalgebras",

abstract = "Let S(m|n,r)Z be a Z-form of a Schur superalgebra S(m|n,r) generated by elements ξi,j. We solve a problem of Muir and describe a Z-form of a simple S(m|n,r)-module Dλ,Q over the field Q of rational numbers, under the action of S(m|n,r)Z. This Z-form is the Z-span of modified bideterminants [Tℓ:Ti] defined in this work. We also prove that each [Tℓ:Ti] is a Z-linear combination of modified bideterminants corresponding to (m|n)-semistandard tableaux Ti.",

author = "Frantisek Marko and Zubkov, \{Alexandr N.\}",

note = "Funding Information: The second author was supported by RFFI 10.01.00383 a. The authors would like to thank a referee for careful reading of the manuscript and helpful suggestions.",

year = "2011",

month = sep,

doi = "10.1016/j.jpaa.2011.02.003",

language = "English (US)",

volume = "215",

pages = "2223--2230",

journal = "Journal of Pure and Applied Algebra",

issn = "0022-4049",

publisher = "Elsevier B.V.",

number = "9",

}

TY - JOUR

T1 - A note on bideterminants for Schur superalgebras

AU - Marko, Frantisek

AU - Zubkov, Alexandr N.

N1 - Funding Information: The second author was supported by RFFI 10.01.00383 a. The authors would like to thank a referee for careful reading of the manuscript and helpful suggestions.

PY - 2011/9

Y1 - 2011/9

N2 - Let S(m|n,r)Z be a Z-form of a Schur superalgebra S(m|n,r) generated by elements ξi,j. We solve a problem of Muir and describe a Z-form of a simple S(m|n,r)-module Dλ,Q over the field Q of rational numbers, under the action of S(m|n,r)Z. This Z-form is the Z-span of modified bideterminants [Tℓ:Ti] defined in this work. We also prove that each [Tℓ:Ti] is a Z-linear combination of modified bideterminants corresponding to (m|n)-semistandard tableaux Ti.

AB - Let S(m|n,r)Z be a Z-form of a Schur superalgebra S(m|n,r) generated by elements ξi,j. We solve a problem of Muir and describe a Z-form of a simple S(m|n,r)-module Dλ,Q over the field Q of rational numbers, under the action of S(m|n,r)Z. This Z-form is the Z-span of modified bideterminants [Tℓ:Ti] defined in this work. We also prove that each [Tℓ:Ti] is a Z-linear combination of modified bideterminants corresponding to (m|n)-semistandard tableaux Ti.

UR - https://www.scopus.com/pages/publications/79953715626

UR - https://www.scopus.com/pages/publications/79953715626#tab=citedBy

U2 - 10.1016/j.jpaa.2011.02.003

DO - 10.1016/j.jpaa.2011.02.003

M3 - Article

AN - SCOPUS:79953715626

SN - 0022-4049

VL - 215

SP - 2223

EP - 2230

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

IS - 9

ER -

A note on bideterminants for Schur superalgebras

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this