TY - JOUR
T1 - On the symmetric Gelfand pair (ℋn× ℋn-1, diag (ℋn-1))
AU - Tout, Omar
N1 - Publisher Copyright:
© 2021 World Scientific Publishing Company.
PY - 2021/5
Y1 - 2021/5
N2 - We show that the ℋn-1-conjugacy classes of ℋn, where ℋn is the hyperoctahedral group on 2n elements, are indexed by marked bipartitions of n. This will lead us to prove that (ℋn ×ℋn-1,diag(ℋn-1)) is a symmetric Gelfand pair and that the induced representation 1diag(ℋn-1)ℋn×ℋn-1 is multiplicity free.
AB - We show that the ℋn-1-conjugacy classes of ℋn, where ℋn is the hyperoctahedral group on 2n elements, are indexed by marked bipartitions of n. This will lead us to prove that (ℋn ×ℋn-1,diag(ℋn-1)) is a symmetric Gelfand pair and that the induced representation 1diag(ℋn-1)ℋn×ℋn-1 is multiplicity free.
KW - Hyperoctahedral group
KW - Symmetric Gelfand pairs
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U2 - 10.1142/S0219498821500857
DO - 10.1142/S0219498821500857
M3 - Article
AN - SCOPUS:85091361891
SN - 0219-4988
VL - 20
JO - Journal of Algebra and Its Applications
JF - Journal of Algebra and Its Applications
IS - 5
M1 - 2150085
ER -