Can 3 dimensional Heisenberg group be represented irreducibly on L^2(S)?
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It is well-known that unitary dual of the 3 dimensional Heisenberg group H represented on $L^2(mathbb{R})$ is given by a nonzero real number $lambdain R^*$(can be interpreted as $1/hbar$). When $lambda=1/hbar=0$, the unirreps are all 1 dimensional. My question is if H can also be represented irreducibly on $L^2(mathbb{S})$ with $mathbb{S}$ denoting the 1 dimensional compact manifold---circle.
representation-theory locally-compact-groups heisenberg-group
asked Dec 20 '18 at 4:27
user78032user78032
184
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$begingroup$
It is well-known that unitary dual of the 3 dimensional Heisenberg group H represented on $L^2(mathbb{R})$ is given by a nonzero real number $lambdain R^*$(can be interpreted as $1/hbar$). When $lambda=1/hbar=0$, the unirreps are all 1 dimensional. My question is if H can also be represented irreducibly on $L^2(mathbb{S})$ with $mathbb{S}$ denoting the 1 dimensional compact manifold---circle.
representation-theory locally-compact-groups heisenberg-group
asked Dec 20 '18 at 4:27
user78032user78032
184
$endgroup$
add a comment |
$begingroup$
It is well-known that unitary dual of the 3 dimensional Heisenberg group H represented on $L^2(mathbb{R})$ is given by a nonzero real number $lambdain R^*$(can be interpreted as $1/hbar$). When $lambda=1/hbar=0$, the unirreps are all 1 dimensional. My question is if H can also be represented irreducibly on $L^2(mathbb{S})$ with $mathbb{S}$ denoting the 1 dimensional compact manifold---circle.
representation-theory locally-compact-groups heisenberg-group
asked Dec 20 '18 at 4:27
user78032user78032
184
$endgroup$
It is well-known that unitary dual of the 3 dimensional Heisenberg group H represented on $L^2(mathbb{R})$ is given by a nonzero real number $lambdain R^*$(can be interpreted as $1/hbar$). When $lambda=1/hbar=0$, the unirreps are all 1 dimensional. My question is if H can also be represented irreducibly on $L^2(mathbb{S})$ with $mathbb{S}$ denoting the 1 dimensional compact manifold---circle.
representation-theory locally-compact-groups heisenberg-group
representation-theory locally-compact-groups heisenberg-group
asked Dec 20 '18 at 4:27
user78032user78032
184
asked Dec 20 '18 at 4:27
user78032user78032
184
edited Dec 20 '18 at 5:40
user78032
asked Dec 20 '18 at 4:27
user78032user78032
184
asked Dec 20 '18 at 4:27
user78032user78032
184
asked Dec 20 '18 at 4:27
user78032user78032
184
184
add a comment |
add a comment |
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