arXiv subjects
Publications and source records attributed to Gordan Savin.
In this paper we develop representation theory of the two fold central extension of SL(2) over the field of 2-adic numbers. As a consequence, we obtain a local Shimura correspondence between the two fold central extension of SL(2) and the linear group PGL(2), which we show to be compatible with the global Shimura correspondence at p=2.
For every finite field F and every positive integer r, there exists a finite extension F' of F such that either SO(2r+1,F') or its simple derived group can be realized as a Galois group over Q. If the characteristic of F is 3 or 5 (mod 8), then we can guarantee that the derived group of SO(2r+1,F') can be realized. Likewise, for every finite field F, there exists a finite extension F' of F such that the finite simple group G_2(F') can be realized a Galois group over Q. The proof uses automorphic forms to construct Galois representations which cut out Galois extensions of the desired type.
Let $G$ be a split simply laced group defined over a $p$-adic field $F$. In this paper we study the restriction of the minimal representation of $G$ to various dual pairs in $G$. For example, the restriction of the minimal representation of $E_7$ to the dual pair $G_2 \times{}$Sp(6) gives the non-endoscopic Langlands lift of irreducible representations of $G_2$ to Sp(6).