Abstract
Abstract
It turns out that harmonic analysis on the superspace
R
m
|
2
n
is quite parallel to the classical theory on the Euclidean space
R
m
unless the superdimension
M
:=
m
−
2
n
is even and non-positive. The underlying symmetry is given by the orthosymplectic superalgebra
o
s
p
(
m
|
2
n
)
. In this paper, when the symmetry is reduced to
o
s
p
(
m
−
1
|
2
n
)
we describe explicitly the corresponding branching laws for spherical harmonics on
R
m
|
2
n
also in exceptional cases, i.e, when
M
−
1
∈
−
2
N
0
. In unexceptional cases, these branching laws are well-known and quite analogous as in the Euclidean framework.
Funder
Grantová Agentura České Republiky
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