Erratum to: Unitary Representations of Super Lie Groups and Applications to the Classification and Multiplet Structure of Super Particles

Communications in Mathematical Physics, Oct 2011

C. Carmeli, G. Cassinelli, A. Toigo, V. S. Varadarajan

A PDF file should load here. If you do not see its contents the file may be temporarily unavailable at the journal website or you do not have a PDF plug-in installed and enabled in your browser.

Alternatively, you can download the file locally and open with any standalone PDF reader:

https://link.springer.com/content/pdf/10.1007%2Fs00220-011-1332-8.pdf

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. - 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)


This is a preview of a remote PDF: https://link.springer.com/content/pdf/10.1007%2Fs00220-011-1332-8.pdf

C. Carmeli, G. Cassinelli, A. Toigo, V. S. Varadarajan. Erratum to: Unitary Representations of Super Lie Groups and Applications to the Classification and Multiplet Structure of Super Particles, Communications in Mathematical Physics, 2011, pp. 565, Volume 307, Issue 2, DOI: 10.1007/s00220-011-1332-8