Erratum to: Unitary Representations of Super Lie Groups and Applications to the Classification and Multiplet Structure of Super Particles
Commun. Math. Phys.
Erratum to: Unitary Representations of Super Lie Groups and Applications to the Classification and Multiplet Structure of Super Particles
C. Carmeli 1 2
G. Cassinelli 1 2
A. Toigo 0 4
V. S. Varadarajan 3
0 Dipartimento di Matematica Francesco Brioschi, Politecnico di Milano , Piazza Leonardo da Vinci 32, 20133 Milano , Italy
1 Istituto Nazionale di Fisica Nucleare, Sezione di Genova , Via Dodecaneso 33, 16146 Genova , Italy
2 Dipartimento di Fisica, Universita di Genova , Via Dodecaneso 33, 16146 Genova , Italy
3 Department of Mathematics, University of California at Los Angeles , Box 951555, Los Angeles, CA 90095-1555 , USA
4 Istituto Nazionale di Fisica Nucleare, Sezione di Milano , Via Celoria 16, 20133 Milano , Italy
Professor Hadi Salmasian has drawn our attention a misstatement in Lemma 1 where the correct statement should be X B B. In the corrigendum below we insert this correction and a small set of consequent corrections in Lemma 1 as well as Propositions 2 and 3. We thank professor Salmasian for this.
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1. p. 222: In item (ii) of Lemma 1, replace such that X B D( X ) with such that
X B B.
2. p. 222: In the last statement of Lemma 1, replace if we only assume that B is
invariant under H and contains a dense set of analytic vectors with if we only assume
that B D( H ) and contains a dense set of analytic vectors for H .
3. p. 222: In the last paragraph of the proof of Lemma 1, replace Finally, let us assume
that H B B and that B contains a dense set of analytic vectors for H with Finally,
let us assume that B D( H ) and that B contains a dense set of analytic vectors
for H .
4. p. 222: In the last paragraph of the proof of Lemma 1, replace we have X 2n =
H n B and X 2n+1 D( X ) by assumption, and with we have D( X n ) for
all n by X -invariance of B, and.
5. p. 226, last paragraph before Proposition 2: In item (b)-(vi), replace ( X )B
D( (Y )) for all X, Y g1 with ( X )B B for all X g1.
6. p. 227, in the proof of Proposition 2: Before the paragraph beginning with It remains
only to show..., add the following paragraph: We now prove that, for all X g1,
the operator ( X ) is odd on C (0). If Pi : H H is the orthogonal
projection onto Hi , then Pi B B, and ( X ) Pi = Pi+1 (mod 2) ( X ) for all B
by item (iii). If C (0) and (n) is a sequence in B such that n and
(X )n (X ) , then Pi n Pi and (X ) Pi n = Pi+1 (mod 2)(X )n
Pi+1 (mod 2)(X ) . Thus we have (X ) Pi = Pi+1 (mod 2)(X ) , and the claim
follows.
7. p. 227, item (i) in the statement of Proposition 2: Replace so that , as in Proposition
(1), is a representation of g in C (0) with so that , as in Proposition 1, restricts
to a representation of g in C (0).
Communicated by Y. Kawahigashi
(...truncated)