Geodesic
SOME IRREDUCIBLE REPRESENTATIONS OF BRAUER'S CENTRALIZER ALGEBRAS
Glasgow mathematical journal, Tome 46 (2004) no. 3, pp. 499-513

Voir la notice de l'article provenant de la source Cambridge

DOI

Let $m, n\in\Bbb N$, $V$ be a $2m$-dimensional complex vector space. The irreducible representations of the Brauer's centralizer algebra $B_n(-2m)$ appearing in $V^{\otimes{n}}$ are in 1–1 correspondence to the set of pairs $(\,f,\lamda)$, where $f\in\Z$ with $0\leq f\leq [n/2]$, $and$ $\lam\vdash n-2f$ satisfying $\lam_1\leq m$. In this paper, we first show that each of these representations has a basis consists of eigenvectors for the subalgebra of $B_n(-2m)$ generated by all the Jucys-Murphy operators, and we determine the corresponding eigenvalues. Then we identify these representations with the irreducible representations constructed from a cellular basis of $B_n(-2m)$. Finally, an explicit description of the action of each generator of $B_n(-2m)$ on such a basis is also given, which generalizes earlier work of [15] for Brauer's centralizer algebra $B_n(m)$.
DOI : 10.1017/S001708950400196X
Mots-clés : 16G99 
HU, JUN; YANG, YICHUAN. SOME IRREDUCIBLE REPRESENTATIONS OF BRAUER'S CENTRALIZER ALGEBRAS. Glasgow mathematical journal, Tome 46 (2004) no. 3, pp. 499-513. doi: 10.1017/S001708950400196X
@article{10_1017_S001708950400196X,
     author = {HU, JUN and YANG, YICHUAN},
     title = {SOME {IRREDUCIBLE} {REPRESENTATIONS} {OF} {BRAUER'S} {CENTRALIZER} {ALGEBRAS}},
     journal = {Glasgow mathematical journal},
     pages = {499--513},
     year = {2004},
     volume = {46},
     number = {3},
     doi = {10.1017/S001708950400196X},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S001708950400196X/}
}
TY  - JOUR
AU  - HU, JUN
AU  - YANG, YICHUAN
TI  - SOME IRREDUCIBLE REPRESENTATIONS OF BRAUER'S CENTRALIZER ALGEBRAS
JO  - Glasgow mathematical journal
PY  - 2004
SP  - 499
EP  - 513
VL  - 46
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S001708950400196X/
DO  - 10.1017/S001708950400196X
ID  - 10_1017_S001708950400196X
ER  - 
%0 Journal Article
%A HU, JUN
%A YANG, YICHUAN
%T SOME IRREDUCIBLE REPRESENTATIONS OF BRAUER'S CENTRALIZER ALGEBRAS
%J Glasgow mathematical journal
%D 2004
%P 499-513
%V 46
%N 3
%U http://geodesic.mathdoc.fr/articles/10.1017/S001708950400196X/
%R 10.1017/S001708950400196X
%F 10_1017_S001708950400196X

Cité par Sources :