TY - JOUR
T1 - A bideterminant basis for a reductive monoid
AU - Tange, Rudolf
PY - 2012/5
Y1 - 2012/5
N2 - We use the rational tableaux introduced by Stembridge to give a bideterminant basis for a normal reductive monoid and for its variety of noninvertible elements. We also obtain a bideterminant basis for the full coordinate ring of the general linear group and for all its truncations with respect to saturated sets. Finally, we deduce an alternative proof of the double centraliser theorem for the rational Schur algebra and the walled Brauer algebra over an arbitrary infinite base field which was first obtained by Dipper, Doty and Stoll. (C) 2011 Elsevier B.V. All rights reserved.
AB - We use the rational tableaux introduced by Stembridge to give a bideterminant basis for a normal reductive monoid and for its variety of noninvertible elements. We also obtain a bideterminant basis for the full coordinate ring of the general linear group and for all its truncations with respect to saturated sets. Finally, we deduce an alternative proof of the double centraliser theorem for the rational Schur algebra and the walled Brauer algebra over an arbitrary infinite base field which was first obtained by Dipper, Doty and Stoll. (C) 2011 Elsevier B.V. All rights reserved.
UR - http://www.scopus.com/inward/record.url?scp=84855835593&partnerID=8YFLogxK
U2 - 10.1016/j.jpaa.2011.10.029
DO - 10.1016/j.jpaa.2011.10.029
M3 - Article
VL - 216
SP - 1207
EP - 1221
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
SN - 0022-4049
IS - 5
ER -