TY - JOUR
T1 - Abstract Young representations for Coxeter groups of type D
AU - Cherniavsky, Yona
N1 - Funding Information:
✩ Supported in part by a grant from the Israel Science Foundation, this work is a part of the author’s PhD thesis, Department of Mathematics and Statistics, Bar-Ilan University, Ramat-Gan 52900, Israel. E-mail addresses: [email protected], [email protected].
PY - 2008/10
Y1 - 2008/10
N2 - Abstract Young (briefly: AY) representations are Coxeter group representations which carry an extended Young form. These representations appear in a new axiomatic approach to the representation theory of Coxeter groups. While AY representations for Coxeter groups of types A and B are well understood, little is known about type D. We introduce D-Young tableaux and study minimal AY representations associated with them. The main result is a decomposition rule for the AY representations which are induced from Sn into Dn. The proof of this rule involves a combinatorial bijection together with theorems from complex analysis.
AB - Abstract Young (briefly: AY) representations are Coxeter group representations which carry an extended Young form. These representations appear in a new axiomatic approach to the representation theory of Coxeter groups. While AY representations for Coxeter groups of types A and B are well understood, little is known about type D. We introduce D-Young tableaux and study minimal AY representations associated with them. The main result is a decomposition rule for the AY representations which are induced from Sn into Dn. The proof of this rule involves a combinatorial bijection together with theorems from complex analysis.
KW - Abstract Young representations
KW - Type-D Coxeter group
KW - Young orthogonal form
UR - http://www.scopus.com/inward/record.url?scp=52949127325&partnerID=8YFLogxK
U2 - 10.1016/j.aam.2007.09.005
DO - 10.1016/j.aam.2007.09.005
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AN - SCOPUS:52949127325
SN - 0196-8858
VL - 41
SP - 561
EP - 583
JO - Advances in Applied Mathematics
JF - Advances in Applied Mathematics
IS - 4
ER -