The structure of certain highest weight modules forSL3
نویسندگان
چکیده
منابع مشابه
Highest-weight Theory: Verma Modules
We will now turn to the problem of classifying and constructing all finitedimensional representations of a complex semi-simple Lie algebra (or, equivalently, of a compact Lie group). It turns out that such representations can be characterized by their “highest-weight”. The first method we’ll consider is purely Lie-algebraic, it begins by constructing a universal representation with a given high...
متن کاملCharacterization of Simple Highest Weight Modules
We prove that for simple complex finite dimensional Lie algebras, affine Kac-Moody Lie algebras, the Virasoro algebra and the Heisenberg-Virasoro algebra, simple highest weight modules are characterized by the property that all positive root elements act on these modules locally nilpotently. We also show that this is not the case for higher rank Virasoro and for Heisenberg algebras.
متن کاملLaplace transform and unitary highest weight modules
The unitarizable modules in the analytic continuation of the holomorphic discrete series for tube type domains are realized as Hilbert spaces obtained through the Laplace transform.
متن کاملCriteria for the Unitarizability of Some Highest Weight Modules
For a linear semisimple Lie group we obtain a necessary and sufficient condition for a highest weight module with non-singular infinitesimal character to be unitarizable.
متن کاملHighest weight modules over W1+∞ algebra and the bispectral problem
This paper is the last of a series of papers devoted to the bispectral problem [3]–[6]. Here we examine the connection between the bispectral operators constructed in [6] and the Lie algebra W1+∞ (and its subalgebras). To give a more detailed idea of the contents of the present paper we briefly recall the results of [4]–[6] which we need. In [4] we built large families of representations of W1+...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1986
ISSN: 0021-8693
DOI: 10.1016/0021-8693(86)90037-2