Check Character Systems Using Chevalley Groups

Identity with Constants in a Chevalley Group of Type F4 v. Nesterov and A. Stepanov

N. L. Gordeev proved that a generalized group identity holds in Chevalley groups with multiply laced root systems. It was also shown that a stronger identity is valid for the Chevalley groups of types Bl and Cl. In the present paper, it is proved that this strong identity is fulfilled in Chevalley groups of type F4 and fails to be true in Chevalley groups of type G2. The main result of the pape...

Monomial Irreducible sln-Modules

In this article, we introduce monomial irreducible representations of the special linear Lie algebra $sln$. We will show that this kind of representations have bases for which the action of the Chevalley generators of the Lie algebra on the basis elements can be given by a simple formula.

ar X iv : 1 20 2 . 02 10 v 1 [ m at h . N T ] 1 F eb 2 01 2 Fourier coefficients of automorphic forms , character variety orbits , and small representations

We consider the Fourier expansions of automorphic forms on general Lie groups, with a particular emphasis on exceptional groups. After describing some principles underlying known results on GL(n), Sp(4), and G2, we perform an analysis of the expansions on split real forms of E6 and E7 where simplifications take place for automorphic realizations of real representations which have small Gelfand-...

A Chevalley-Warning Approach to P-adic Estimates of Character Sums

On check character systems over quasigroups and loops

In this article we study check character systems that is error detecting codes, which arise by appending a check digit an to every word a1a2...an−1 : a1a2...an−1 → a1a2...an−1an with the check formula (...((a1 · δa2) · δ 2a3)...) · δ n−2an−1) · δ n−1an = c, where Q(·) is a quasigroup or a loop, δ is a permutation of Q, c ∈ Q. We consider detection sets for such errors as transpositions (ab → ba...