The tensor algebra of the identity representation as a~module over the Lie superalgebras $\mathfrak Gl(n,m)$ and~$Q(n)$
Sbornik. Mathematics, Tome 51 (1985) no. 2, pp. 419-427
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Let $T$ be the tensor algebra of the identity representation of the Lie superalgebras in the series $\mathfrak Gl$ and $Q$. The method of Weyl is used to construct a correspondence between the irreducible representations (respectively, the irreducible projective representations) of the symmetric group and the irreducible $\mathfrak Gl$- (respectively, $Q$-) submodules of $T$. The properties of the representations are studied on the basis of this correspondence. A formula is given for the characters on the irreducible $Q$-submodules of $T$.
Bibliography: 8 titles.
@article{SM_1985_51_2_a6,
author = {A. N. Sergeev},
title = {The tensor algebra of the identity representation as a~module over the {Lie} superalgebras $\mathfrak Gl(n,m)$ and~$Q(n)$},
journal = {Sbornik. Mathematics},
pages = {419--427},
publisher = {mathdoc},
volume = {51},
number = {2},
year = {1985},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1985_51_2_a6/}
}
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%0 Journal Article %A A. N. Sergeev %T The tensor algebra of the identity representation as a~module over the Lie superalgebras $\mathfrak Gl(n,m)$ and~$Q(n)$ %J Sbornik. Mathematics %D 1985 %P 419-427 %V 51 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/SM_1985_51_2_a6/ %G en %F SM_1985_51_2_a6
A. N. Sergeev. The tensor algebra of the identity representation as a~module over the Lie superalgebras $\mathfrak Gl(n,m)$ and~$Q(n)$. Sbornik. Mathematics, Tome 51 (1985) no. 2, pp. 419-427. http://geodesic.mathdoc.fr/item/SM_1985_51_2_a6/