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A quantum fermion realisation of the finite dimensional spinor representation of U q ( o s p ( 1 | 2 n ) )
The quantum supergroup U q ( o s p ( 1 | 2 n ) ) admits a finite dimensional spinor representation, which does not have a classical limit. We construct a realisation of this representation on the Fock space of q-fermions. We also generalise the construction to the infinite dimensional spinor represe...
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| Published in: | Journal of mathematical physics 2017-07, Vol.58 (7) |
|---|---|
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Online Access: | Get full text |
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| Summary: | The quantum supergroup
U
q
(
o
s
p
(
1
|
2
n
)
)
admits a finite dimensional spinor representation, which does not have a classical limit. We construct a realisation of this representation on the Fock space of q-fermions. We also generalise the construction to the infinite dimensional spinor representations of
U
q
(
o
s
p
(
2
m
+
1
|
2
n
)
)
for
m
,
n
≥
1
by using both quantum bosons and fermions. This leads to a new realisation different from those obtained before by other researchers. |
|---|---|
| ISSN: | 0022-2488 1089-7658 |
| DOI: | 10.1063/1.4991678 |