We provide formulas for the denominator and superdenominator of a basic classical type Lie superalgebra for any set of positive roots. We establish a connection between certain sets of positive roots and the theory of reductive dual pairs of real Lie groups, and, as an application of these formulas, we recover the Theta correspondence for compact dual pairs. Along the way we give an explicit description of the real forms of basic classical type Lie superalgebras.

中文翻译：

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有限维李超代数的分母身份和紧凑对对的Howe对偶

我们为任何一组正根提供基本经典类型李超代数的分母和超分母的公式。我们在某些正根集与真实李群的还原对偶对理论之间建立联系，并且，通过应用这些公式，我们恢复了紧凑对偶的Theta对应关系。在此过程中，我们对基本古典类型李超代数的实际形式进行了明确的描述。