arXiv subjects

J. Thierry-Mieg

Publications and source records attributed to J. Thierry-Mieg.

3 recordsLinked to original sources

arXiv2019

On superdimensions of some infinite-dimensional irreducible representations of $osp(m|n)$

In a recent paper characters and superdimension formulas were investigated for the class of representations with Dynkin labels $[0,\ldots,0,p]$ of the Lie superalgebra $osp(m|n)$. Such representations are infinite-dimensional, and of relevance in supergravity theories provided their superdimension is finite. We have shown that the superdimension of such representations coincides with the dimension of a $so(m-n)$ representation. In the present contribution, we investigate how this $osp(m|n)\sim so(m-n)$ correspondence can be extended to the class of $osp(2m|2n)$ representations with Dynkin labels $[0,\ldots,0,q,p]$.

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arXiv2019

On characters and superdimensions of some infinite-dimensional irreducible representations of $\mathfrak{osp}(m|n)$

Chiral spinors and self dual tensors of the Lie superalgebra $\mathfrak{osp}(m|n)$ are infinite dimensional representations belonging to the class of representations with Dynkin labels $[0,\ldots,0,p]$. We have shown that the superdimension of $[0,\ldots,0,p]$ coincides with the dimension of a $\mathfrak{so}(m-n)$ representation. When the superdimension is finite, these representations could play a role in supergravity models. Our technique is based on expansions of characters in terms of supersymmetric Schur functions. In the process of studying these representations, we obtain new character expansions.

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arXiv2017

Extension of the osp(m|n)~ so(m-n) Correspondence to the Infinite-Dimensional Chiral Spinors and Self Dual Tensors

The spinor representations of the orthosymplectic Lie superalgebras osp(m|n) are considered and constructed. These are infinite-dimensional irreducible representations, of which the superdimension coincides with the dimension of the spinor representation of so(m-n). Next, we consider the self dual tensor representations of osp(m|n) and their generalizations: these are also infinite-dimensional and correspond to the highest irreducible component of the $p^{th}$ power of the spinor representation. We determine the character of these representations, and deduce a superdimension formula. From this, it follows that also for these representations the osp(m|n)~ so(m-n) correspondence holds.

math-ph↗