Much can be learned about a finite group from its character table, but sometimes that table can be difficult to compute. Supercharacter theories are generalizations of character theory, defined by P. Diaconis and I.M. Isaacs in [8], in which certain (possibly reducible) characters called supercharacters take the place of the irreducible characters, and a certain coarser partition of the group t...

We define the commuting algebra determinant of a finite group action on a finite set, a notion dual to the group determinant of Dedekind. We show that the following combinatorial example is a commuting algebra determinant. Let Bq(n) denote the set of all subspaces of an n-dimensional vector space over Fq. The type of an ordered pair (U, V ) of subspaces, where U, V ∈ Bq(n), is the ordered tripl...

We recursively determine the homotopy type of space any irreducible framed link in 3-sphere, modulo rotations. This leads us to knot solid torus, thus answering a question posed by Arnold. similarly study spaces unframed links rotations, and knots thickened torus. The subgroup meridional rotations splits as direct factor fundamental group except unknot. Its generators can be viewed generalizati...

We consider three-dimensional elastic frames constructed out of Euler–Bernoulli beams and describe a simple process generating joint conditions the geometric description frame. The corresponding differential operator is shown to be self-adjoint. In special case planar frames, decomposes into direct sum two operators, one coupling out-of-plane displacement angular (torsional) other in-plane with...

Let $A$ be an abelian surface and let $G$ a finite group of automorphisms fixing the origin. Assume that analytic representation is irreducible. We give classification pairs $(A,G)$ such quotient $A/G$ smooth. In particular, we prove $A=E^2$ with $E$ elliptic curve $A/G\simeq\mathbb{P}^2$ in all cases. Moreover, for fixed $E$, there are only finitely many $(E^2,G)$ up to isomorphism. This fills...

Let K denote a field, and let V denote a vector space over K with finite positive dimension. We consider a pair of linear transformations A : V → V and A : V → V that satisfy both conditions below: (i) There exists a basis for V with respect to which the matrix representing A is diagonal and the matrix representing A is irreducible tridiagonal. (ii) There exists a basis for V with respect to wh...

According to the classical theorem, every algebraic variety endowed with a nontrivial rational action of a connected linear algebraic group is birationally isomorphic to a product of another algebraic variety and Ps with positive s. We show that the classical proof of this theorem actually works only in characteristic 0 and we give a characteristic free proof of it. To this end we prove and use...

This is an expository paper on tensor products where the standard approaches for constructing concrete instances of algebraic linear spaces, via quotient spaces or maps bilinear maps, are reviewed by reducing them to different but isomorphic interpretations abstract notion, viz. universal property, which based a pair axioms.

The evolutionary algorithm stochastic process is well-known to be Markovian. These have been under investigation in much of the theoretical evolutionary computing research. When mutation rate is positive, the Markov chain modeling an evolutionary algorithm is irreducible and, therefore, has a unique stationary distribution. Rather little is known about the stationary distribution. In fact, the ...

In this paper we determine the support of the irreducible spherical representation (i.e., the irreducible quotient of the polynomial representation) of the rational Cherednik algebra of a finite Coxeter group for any value of the parameter c. In particular, we determine for which values of c this representation is finite dimensional. This generalizes a result of Varagnolo and Vasserot, [VV], wh...