Related papers: Character stacks are PORC count

We count points on character varieties associated with punctured surfaces and regular semisimple generic conjugacy classes in reductive groups. We find that the number of points are palindromic polynomials. This suggests a $P=W$ conjecture…

This book describes some computational methods to deal with modular characters of finite groups. It is the theoretical background of the MOC system of the same authors. This system was, and is still used, to compute the modular character…

We prove that the number of groups of order $p^n$ whose Frattini subgroup is central is for fixed $n$ a PORC (`polynomial on residue classes') function of $p$. This extends a result of G. Higman.

In the first chapters, this paper contains a survey on the theory of ordinary characters of finite reductive groups with non-connected centre. The last chapters are devoted to the proof of Lusztig's conjecture on characteristic functions of…

Character polynomials are used to study the restriction of a polynomial representation of a general linear group to its subgroup of permutation matrices. A simple formula is obtained for computing inner products of class functions given by…

Using a general result of Lusztig, we find the decomposition into irreducibles of certain induced characters of the projective general linear group over a finite field of odd characteristic.

In this paper, we extend the Topological Quantum Field Theory developed by Gonz\'alez-Prieto, Logares, and Mu\~noz for computing virtual classes of $G$-representation varieties of closed orientable surfaces in the Grothendieck ring of…

In 1952, Perron showed that quadratic residues in a field of prime order satisfy certain ad- ditive properties. This result has been generalized in different directions, and our contribution is to provide a further generalization concerning…

Block character of a finite symmetric group S(n) is a positive definite function which depends only on the number of cycles in permutation. We describe the cone of block characters by identifying its extreme rays, and find relations of the…

As shown by Bonnaf\'e, a step in proving a Jordan decomposition of characters of finite special linear groups is the parametrization of unipotent characters of centralizers of semi-simple elements in projective linear groups. We show the…

We show that for every subset $E$ of positive density in the set of integer square-matrices with zero traces, there exists an integer $k \geq 1$ such that the set of characteristic polynomials of matrices in $E-E$ contains the set of…

Let $\bf{G}$ be a connected reductive group with connected center defined over $\mathbb{F}_q$, with Frobenius morphism $F$. We parameterize all of the real-valued irreducible complex characters of ${\bf G}^F$ using the Jordan decomposition…

We use character polynomials to obtain a positive combinatorial interpretation of the multiplicity of the sign representation in irreducible polynomial representations of $GL_n(\mathbb{C})$ indexed by two-column and hook partitions. Our…

In this paper we obtained the formula for the number of irreducible polynomials with degree $n$ over finite fields of characteristic two with given trace and subtrace. This formula is a generalization of the result of Cattell et al.(2003)…

We compute the E-polynomial of the character variety of representations of a rank r free group in SL(3, C). Expanding upon existing techniques, we stratify the space of representations and compute the E-polynomial of each geometrically…

Representation theory of the symmetric group $\mathfrak{S}_n$ has a very distinctive combinatorial flavor. The conjugacy classes as well as the irreducible characters are indexed by integer partitions $\lambda \vdash n$. We introduce class…

We obtain nontrivial estimates of quadratic character sums of division polynomials $\Psi_n(P)$, $n=1,2, ...$, evaluated at a given point $P$ on an elliptic curve over a finite field of $q$ elements. Our bounds are nontrivial if the order of…

We initiate the study of characters of surface groups and their corresponding tracial representations. We show that any tracial representation can be approximated arbitrarily well in the Wasserstein topology by factorial tracial…

There is a digraph corresponding to every square matrix over $\mathbb{C}$. We generate a recurrence relation using the Laplace expansion to calculate the characteristic, and permanent polynomials of a square matrix. Solving this recurrence…

We develop the concept of character level for the complex irreducible characters of finite, general or special, linear and unitary groups. We give characterizations of the level of a character in terms of its Lusztig's label and in terms of…