A Classification of Unitary Highest Weight Modules

Enright, Thomas J.; Howe, Roger; Wallach, Nolan R.

doi:10.1007/978-1-4684-6730-7_7

Cited by 191 publications

(193 citation statements)

References 8 publications

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“…One may also consider other discrete representations. A natural choice is the class of unitary representations for Hermitian symmetric spaces considered in [23] and [20]. Then the irreducible g C -module will be unitary and we avoid the problems encountered above.…”

Section: The Gko Coset Constructionmentioning

confidence: 99%

On the unitarity of gauged non-compact WZNW strings

Björnsson

Hwang

2008

Nuclear Physics B

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In this paper we investigate the unitarity of gauged non-compact WZNW strings i.e. string theories formulated as G/H ′ WZNW models, where G is a non-compact group. These models represent string theories on non-trivial curved space-times with one time-like component. We will prove that for the class of models connected to Hermitian symmetric spaces, and a natural set of discrete highest weight representations, the BRST formulation, in which the gauging is defined through a BRST condition, yields unitarity. Unitarity requires the level times the Dynkin index to be an integer, as well as integer valued highest weights w.r.t. the compact subalgebra. We will also show that the BRST formulation is not equivalent to the conventional GKO coset formulation, defined by imposing a highest weight condition w.r.t. H ′ . The latter leads to non-unitary physical string states. This is, to our knowledge, the first example of a fundamental difference between the two formulations.

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Section: The Gko Coset Constructionmentioning

confidence: 99%

On the unitarity of gauged non-compact WZNW strings

Björnsson

Hwang

2008

Nuclear Physics B

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“…First, let us recall that the unitarity conditions for generalised Verma modules of so(2, d) (i.e., in its discrete series of representations) induced from the compact subalgebra so(2) ⊕ so(d) were derived independently in [57][58][59] and in [106] (where the more general result of [107] giving unitarity conditions for highest weight modules of Hermitian algebras was applied to so(2, d)). The outcome of these analyses is that the irreducible modules D ∆ ; which are unitary are: …”

Section: Unitary Higher-spin Singletonsmentioning

confidence: 99%

“…and will decompose their product as the sum of the characters of the different modules appearing in (107) and (109). To do so, the idea is simply to look at the product of (110) and (111), decompose the tensor product of the so(4) characters, and finally recognize the resulting expression as a sum of characters of:…”

Section: Flato-frønsdal Theoremmentioning

confidence: 99%

A Note on Rectangular Partially Massless Fields

Basile

2018

Universe

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Abstract:We study a class of non-unitary so(2, d) representations (for even values of d), describing mixed-symmetry partially massless fields which constitute natural candidates for defining higher-spin singletons of higher order. It is shown that this class of so(2, d) modules obeys of natural generalisation of a couple of defining properties of unitary higher-spin singletons. In particular, we find out that upon restriction to the subalgebra so(2, d − 1), these representations branch onto a sum of modules describing partially massless fields of various depths. Finally, their tensor product is worked out in the particular case of d = 4, where the appearance of a variety of mixed-symmetry partially massless fields in this decomposition is observed.

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“…Much is known about these representations. They were classified in 1980 (5,6). Their characters and cohomology formulas were determined a decade later (7-9).…”

Section: Gelfand-kirillov Dimensionmentioning

confidence: 99%