The (p+, p−) singlet algebra is a vertex operator algebra that is strongly generated by a Virasoro field of central charge 1− 6(p+− p−) /p+p− and a single Virasoro primary field of conformal weight (2p+−1)(2p−−1). Here, the modular properties of the characters of the uncountably many simple modules of each singlet algebra are investigated and the results used as the input to a continuous analog...

1.1. The case ` 6= p. In this case, we are in the setting of the classical Local Langlands Correspondence, which can be stated (roughly) as follows: Let n ≥ 1. We then have an injective map (1)  continuous representations of Gal(Qp/Qp) on n-dimensional Q`-vector spaces, up to isomorphism  ↪−→  irreducible, admissible representations of GLn(Qp) on Q`-vector spaces, up to isomor...

Let fnew be a classical newform of weight ≥2 and prime to p level. We study the arithmetic its unique p-stabilisation f when is p-irregular, that is, Hecke polynomial at admits single repeated root. In particular, we p-adic families through base-change an imaginary quadratic field F where splits, prove respective eigencurves are both Gorenstein f. use this construct two-variable L-function over...