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SPLITTING FIELDS OF CHARACTERISTIC POLYNOMIALS OF RANDOM ELEMENTS IN ARITHMETIC GROUPS
SPLITTING FIELDS CHARACTERISTIC POLYNOMIALS RANDOM ELEMENTS ARITHMETIC GROUPS
2015/8/26
We discuss rather systematically the principle, implicit in earlier works, that for a “random” element in an arithmetic subgroup of a (split, say) reductive algebraic group over a number field, the sp...
A GROWTH MODEL,A GAME,AN ALGEBRA,LAGRANGE INVERSION,AND CHARACTERISTIC CLASSES
Growth model games algebra Lagrange inversion feature classes
2015/7/14
A GROWTH MODEL,A GAME,AN ALGEBRA,LAGRANGE INVERSION,AND CHARACTERISTIC CLASSES.
The first $L^2$-Betti number and approximation in arbitrary characteristic
First L2-Betti number approximation in prime characteristic Group Theory
2012/6/19
Let G be a finitely generated group and (G_i) a descending chain of finite index normal subgroups of G. Given a field K, we consider the sequence b_1(G_i;K)/[G:G_i] of normalized first Betti numbers o...
Category O for Rational Cherednik Algebras H_{t,c}(GL_2(F_p),h) in Characteristic p
Rational Cherednik Algebras Characteristic p Representation Theory
2011/9/23
Abstract: In this paper we describe the characters of irreducible objects in category O for the rational Cherednik algebra associated to GL_2(F_p) over an algebraically closed field of positive charac...
Young's seminormal form and simple modules for $S_n$ in characteristic $p$
Young's seminormal form simple modules characteristic $p$ Quantum Algebra
2011/9/9
Abstract: We realize the integral Specht modules for the symmetric group $S_n$ as induced modules from the subalgebra of the group algebra generated by the Jucys-Murphy elements. We deduce from this t...
Representations of Rational Cherednik Algebras in Positive Characteristic
Rational Cherednik Algebras Positive Characteristic Representation Theory
2011/8/24
Abstract: We study rational Cherednik algebras over an algebraically closed field of positive characteristic. We first prove several general results about category O, and then focus on rational Chered...
Essential dimension of simple algebras in positive characteristic
Essential dimension simple algebras positive characteristic
2011/2/24
Let p be a prime integer, 1 ≤ s ≤ r integers, F a field of characteristic p.
Cech cocycles for differential characteristic classes -- An infinity-Lie theoretic construction
Cech cocycles differential characteristic classes
2010/11/24
We define for every L-infinity algebra a smooth infinity-group integrating it, and define smooth principal infinity-bundles with connection. For every L-infinity-algebra cocycle of suitable degree, we...
Minimal characteristic bisets and finite groups realizing Ruiz-Viruel exotic fusion systems
finite groups realizing Ruiz-Viruel exotic fusion systems
2010/11/23
Continuing our previous work, we determine a minimal left characteristic biset $X$ for every exotic fusion system $\mathcal{F}$ on the extraspecial group $S$ of order $7^3$ and exponent $7$ discovered...
On the mean Euler characteristic of contact manifolds
the mean Euler characteristic contact manifolds
2010/11/23
We express the mean Euler characteristic of a contact structure in terms of the mean indices of closed Reeb orbits for a broad class of contact manifolds, the so-called asymptotically finite contact ...
In prime characteristic we introduce the notion of restricted pre-Lie algebra. We prove in the pre-Lie context the analogue to Jacobson's theorem for restricted Lie algebras. In particular, we prove t...
On the stability of weight spaces of enveloping algebra in prime characteristic
enveloping algebra prime characteristic
2010/11/15
By the result of Dixmier, any weight space of enveloping algebra of Lie algebra L over a field of characteristic 0 is adL stable. In this paper we will show that this result need not be true, if F is...
Euler characteristic of the bifurcation set for a polynomial of degree 2 or 3
Euler characteristic the bifurcation set polynomial
2010/11/11
Assume that the coefficients of a polynomial in a complex variable are Laurent polynomials in some complex parameters. The parameter space (a complex torus) splits into strata corresponding to differ...
Parity conjectures for elliptic curves over global fields of positive characteristic
Parity conjectures elliptic curves positive characteristic
2010/11/19
We prove the $p$-parity conjecture for elliptic curves over global fields of characteristic $p > 3$. We also present partial results on the $\ell$-parity conjecture for primes $\ell \neq p$.
Computing invariants via slicing groupoids: Gel'fand MacPherson, Gale and positive characteristic stable maps
Computing invariants via slicing groupoids Gel'fand MacPherson
2010/11/22
We offer a groupoid-theoretic approach to computing invariants. We illustrate this approach by describing the Gel'fand-MacPherson correspondence and the Gale transform as well as giving Zariski-local...