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On characters of irreducible unitary representations of general linear groups. (English) Zbl 0856.22026
The author reduces the determination of the characters of irreducible unitary representations of $$\text{GL}(n)$$ over a non-Archimedean local field to the determination of the characters of the irreducible square integrable representations of $$\text{GL}(m)$$ with $$m\leq n$$. He also obtains a formula expressing the characters of irreducible unitary representations in terms of the characters of the segment representations of Zelevinsky. This formula generalizes the classical formula for the Steinberg character of $$\text{GL}(n)$$. To obtain his results, he uses a clever trick based on the formal similarity of the unitary duals in the Archimedean and the non-Archimedean case and a result of Gregg Zuckerman expressing the character of the trivial representation as a linear combination of standard characters for $$\text{GL}(n)$$ over complex numbers.

##### MSC:
 2.2e+51 Representations of Lie and linear algebraic groups over local fields
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##### References:
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