Abstract The concept of spin model is due to V. F. R. Jones. The concept of nonsymmetric spin model, which generalizes that of the original (symmetric) spin model, is defined naturally. In this paper, we first determine the diagonal matrices T satisfying the modular invariance or the quasi modular invariance property, i.e., (PT) = s/rnP or (PT) = m%I (respectively), for the character table P of...

Let G $G$ be a finite group and p $p$ q $q$ different primes. Assume that is odd ( , ) ≠ 2 3 $(p,q) \ne (2,3)$ . We prove if divides the degrees of nonlinear irreducible -modular representations, then has normal -complement.

We determine the automorphism group of the split Cartan modular curves Xsplit(p) for all primes p.

We show that the systems of prime-to-p Hecke eigenvalues arising from automorphic forms $$\pmod p$$ for a good prime p associated to an algebraic group $$G/{\mathbb {Q}}$$ Hodge type are same as those modular inner form G.

In his letter [Ser96], J.-P. Serre proves that the systems of Hecke eigenvalues given by modular forms (mod p) are the same as the ones given by locally constant functions A×B/B × → F̄p, where B is the endomorphism algebra of a supersingular elliptic curve. After giving a detailed exposition of Serre’s result, we prove that the systems of Hecke eigenvalues given by Siegel modular forms (mod p) o...

We consider an exhaustion of the modular orbifold by compact subsurfaces and show that growth rate, in terms word length, reciprocal geodesics on such (so named low lying geodesics) converges to rate full set orbifold. derive a similar result for their convergence closed