Related papers: Block characters of the symmetric groups

We examine the large $N$ 1/4-BPS spectrum of the symmetric orbifold CFT Sym$^N(M)$ deformed to the supergravity point in moduli space for $M= K3$ and $T^4$. We consider refinement under both left- and right-moving $SU(2)_R$ symmetries of…

In an earlier paper [1] it was shown that the Frobenius compound characters for the symmetric groups are related to the irreducible characters by a linear relation that involves a unitriagular coupling matrix that gives the Frobenius…

The strong symmetric genus of a finite group is the minimum genus of a compact Riemann surface on which the group acts as a group of automorphisms preserving orientation. A characterization of the infinite number of groups with strong…

Let $G$ be a finite group and let $c(G)$ be the number of cyclic subgroups of $G$. We study the function $\alpha(G) = c(G)/|G|$. We explore its basic properties and we point out a connection with the probability of commutation. For many…

We find an explicit combinatorial interpretation of the coefficients of Kerov character polynomials which express the value of normalized irreducible characters of the symmetric groups S(n) in terms of free cumulants R_2,R_3,... of the…

Stanley considered suitably normalized characters of the symmetric groups on Young diagrams having a special geometric form, namely multirectangular Young diagrams. He proved that the character is a polynomial in the lengths of the sides of…

If a finite group $A$ acts coprimely as automorphisms on a finite group $G$, then the $A$-invariant Brauer $p$-blocks of $G$ are exactly those that contain $A$-invariant irreducible characters.

For an arbitrary infinite field k of characteristic p > 0, we describe the structure of a block of the algebraic monoid M_n(k) (all n x n matrices over k), or, equivalently, a block of the Schur algebra S(n,p), whose simple modules are…

In this paper, we define a set which has a finite group action and is generated by a finite color set, a set which has a finite group action, and a subset of the set of non negative integers. we state its properties to apply one of solution…

If all of the entries of a large $S_n$ character table are covered up and you are allowed to uncover one entry at a time, then how can you quickly identify all of the indexing characters and conjugacy classes? We present a fast algorithmic…

Consider the lattice of all Young diagrams ordered by inclusion, and denote by Y its Hasse graph. Using the Pieri formula for Jack symmetric polynomials, we endow the edges of the graph Y with formal multiplicities depending on a real…

The families of characters, defined by Lusztig for Weyl groups, play an important role in the representation theory of finite reductive groups. The definition of Rouquier for the families of characters in terms of blocks of the Hecke…

We classify the finite groups $G$ which satisfies the condition that every complex irreducible character,whose degree's square doesn't divide the index of its kernel in $G$, lies in the same Galois conjugacy class.

We give a new proof for the description of the blocks in the category of representations of a reductive algebraic group $\mathbf{G}$ over a field of positive characteristic $\ell$ (originally due to Donkin), by working in the Satake…

We study conformal blocks of conformal field theories with a W3 symmetry algebra in the limit where the central charge is large. In this limit, we compute the four-point block as a special case of an sl3-invariant function. In the case when…

Let $G$ be a finite group and let $k$ be a sufficiently large finite field. Let $R(G)$ denote the character ring of $G$ (i.e. the Grothendieck ring of the category of ${\mathbb{C}}G$-modules). We study the structure and the representations…

The object of this short note is to prove a theorem and present a conjecture for the number of even entries in the character table of the symmetric group.

Let $\mathbb{F}_2^\omega$ denote the countably infinite dimensional vector space over the two element field and $\operatorname{GL}(\omega, 2)$ its automorphism group. Moreover, let $\operatorname{Sym}(\mathbb{F}_2^\omega)$ denote the…

We present an explicit formula for subregular characters (i.e, irreducible finite-dimensional complex characters of submaximal degree) of the unitriangular group over a finite field of sufficiently large characteristic.

We study invariant theory of the general linear supergroup in positive characteristic. In particular, we determine when the symmetric group algebra acts faithfully on tensor superspace and demonstrate that the symmetric group does not…