M ay 2 00 8 Admissible unitary completions of locally Q p - rational representations of GL 2 ( F )

7 M ay 2 00 3 Canonical factorization and diagonalization of Baxterized braid matrices : Explicit constructions and applications

Braid matricesˆR(θ), corresponding to vector representations, are spectrally decomposed obtaining a ratio f i (θ)/f i (−θ) for the coefficient of each projector P i appearing in the decomposition. This directly yields a factorization (F (−θ)) −1 F (θ) for the braid matrix, implying also the relationˆR(−θ) ˆ R(θ) = I.This is achieved for GL q (n), SO q (2n + 1), SO q (2n), Sp q (2n) for all n an...

2 8 M ay 2 00 8 UNITARY BRAID REPRESENTATIONS WITH FINITE IMAGE

We characterize unitary representations of braid groups Bn of degree linear in n and finite images of such representations of degree exponential in n.

REPRESENTATIONS OF CLASSICAL p-ADIC GROUPS

Preface 1 1. Classical groups 4 2. Parabolic induction 10 3. Admissible representations 16 4. Jacquet modules and cuspidal representations 24 5. Composition series of induced representations of SL(2, F ) and GL(2, F ) 34 6. Some examples 39 7. Parabolically induced representations of SL(2, F ) and GL(2, F ) 45 8. Some general consequences 52 9. GL(n, F ) 55 10. GSp(n, F ) 62 11. On the reducibi...

2 00 8 On some crystalline representations of GL 2 ( Q p ) Vytautas

ON REPRESENTATION THEORY OF GL(n) OVER p-ADIC DIVISION ALGEBRA AND UNITARITY IN JACQUET-LANGLANDS CORRESPONDENCE

Let F be a p-adic field of characteristic 0, and let A be an F -central division algebra of dimension dA over F . In the paper we first develop the representation theory of GL(m,A), assuming that holds the conjecture which claims that unitary parabolic induction is irreducible for GL(m,A)’s. Among others, we obtain the formula for characters of irreducible unitary representations of GL(m,A) in ...