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).
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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).