Free pro-p groups with operators.
Frobenius n-group algebras
Frobenius algebras play an important role in the representation theory of finite groups. In the present work, we investigate the (quasi) Frobenius property of n-group algebras. Using the (quasi-) Frobenius property of ring, we can obtain some information about constructions of module category over this ring ([2], p. 66-67).
Frobenius symbols for partitions and degrees of spin characters.
From double Hecke algebra to analysis.
Fully commutative Kazhdan-Lusztig cells
We investigate the compatibility of the set of fully commutative elements of a Coxeter group with the various types of Kazhdan-Lusztig cells using a canonical basis for a generalized version of the Temperley-Lieb algebra.
Functional Equation for Spherical Functions on Finite Groups.
Functor categories and group representations
-nilpotent units of commutative group rings
Suppose is a commutative unital ring and is an abelian group. We give a general criterion only in terms of and when all normalized units in the commutative group ring are -nilpotent. This extends recent results published in [Extracta Math., 2008–2009] and [Ann. Sci. Math. Québec, 2009].
G-Actions on Disks and Permuation Representations. II.
G-algebras, Jacobson radical and almost split sequences.
Galois module structure of generalized jacobians.
For a prime number l and for a finite Galois l-extension of function fields L / K over an algebraically closed field of characteristic p <> l, it is obtained the Galois module structure of the generalized Jacobian associated to L, l and the ramified prime divisors. In the cyclic case an implicit integral representation of the Jacobian is obtained and this representation is compared with the explicit representation.
Galois module structure of ideals in wildly ramified cyclic extensions of degree
Galois module structure of ideals in wildly ramified cyclic extensions of degree
For , any totally ramified cyclic extension of degree of local fields which are finite extensions of the field of -adic numbers, we describe the -module structure of each fractional ideal of explicitly in terms of the indecomposable -modules classified by Heller and Reiner. The exponents are determined only by the invariants of ramification.
Galois module structure of the rings of integers in wildly ramified extensions
The main results of this paper may be loosely stated as follows.Theorem.— Let and be sums of Galois algebras with group over algebraic number fields. Suppose that and have the same dimension and that they are identical at their wildly ramified primes. Then (writing for the maximal order in )In many cases The role played by the root numbers of and at the symplectic characters of in determining the relationship between the -modules and is described. The theorem includes...
Galois realization of central extensions of the symmetric group with kernel a cyclic 2-group
Galois-Cohen-Lenstra heuristics
Gelfand-Graev characters of the finite unitary groups.
Generalisations of the Tits representation.
Generalised Magnus modules over the braid group.
Generalizations of morphic group rings.