For every level-zero Bernstein component of GL_n(F), the typical representations are exactly the irreducible subrepresentations of the induced Bushnell-Kutzko type ind_{P_I(1)}^{GL_n(O_F)}(τ_I).
Bushnell and Guy Henniart, The local L anglands conjecture for GL(2) , Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol
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Typical representations for level zero Bernstein components of ${\rm GL}_n(F)$
For every level-zero Bernstein component of GL_n(F), the typical representations are exactly the irreducible subrepresentations of the induced Bushnell-Kutzko type ind_{P_I(1)}^{GL_n(O_F)}(τ_I).