zbMATH — the first resource for mathematics

Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
Unitary representations of $W$ infinity algebras. (English) Zbl 0972.81554
Summary: We study the irreducible unitary highest weight representations, which are obtained from free field realizations, of $W$ infinity algebras $\left({W}_{\infty },{W}_{1+\infty },{W}_{\infty }^{1,1},{W}_{\infty }^{M},{W}_{1+\infty }^{N},{W}_{\infty }^{M,N}\right)$ with central charges $\left(2,1,3,2M,N,2M+N\right)$. The characters of these representations are computed. We contruct a new extended superalgebra ${W}_{\infty }^{M,N}$, whose bosonic sector is ${W}_{\infty }^{M}\otimes {W}_{1+\infty }^{N}$. Its representations obtained from a free field realization with central charge $2M+N$, are classified into two classes: continuous series and discrete series. For the former there exists a supersymmetry, but for the latter a supersymmetry exists only for $M=N$.
MSC:
 81R10 Infinite-dimensional groups and algebras motivated by physics 17B68 Virasoro and related algebras 81T40 Two-dimensional field theories, conformal field theories, etc.