相关论文: An exposition of results of Fricke

Trace maps of two-letter substitution rules are investigated with special emphasis on the underlying algebraic structure and on the existence of invariants. We illustrate the results with the generalized Fibonacci chains and show that the…

This paper introduces calibrated representations for affine Hecke algebras and classifies and constructs all finite dimensional irreducible calibrated representations. The primary technique is to provide indexing sets for controlling the…

We prove a convolution formula for the conjugacy classes in symmetric groups conjectured by the second author. A combinatorial interpretation of coefficients is provided. As a main tool we introduce new semigroup of partial permutations. We…

This article examines matrices whose entries are determined by recursive relations of the form $A_{i, j} = x A_{i, j-1} + y A_{i-1, j-1} + z A_{i-1, j}$, where $x, y, z$ are constants, and the initial conditions are defined along the first…

This paper has been withdrawn because of a gap in the proof of Lemma 3.10. The main reults in this paper have now been proved, and extended in the following papers: S. Ariki and A. Mathas, The number of simple modules of the Hecke algebras…

The affine Grassmannian of $SL_n$ admits an embedding into the Sato Grassmannian, which further admits a Pl\"ucker embedding into the projectivization of Fermion Fock space. Kreiman, Lakshmibai, Magyar, and Weyman describe the linear part…

Using suitable convex functions, we construct a new family of flat Minkowski planes whose automorphism groups are at least $3$-dimensional. These planes admit groups of automorphisms isomorphic to the direct product of $\mathbb{R}$ and the…

The convolution of indicators of two conjugacy classes on the symmetric group S_q is usually a complicated linear combination of indicators of many conjugacy classes. Similarly, a product of the moments of the Jucys--Murphy element involves…

We consider algebras over a field K, generated by two variables x and y subject to the single relation yx = qxy + ax + by + c for q in K^* and a, b, c in K. We prove, that among such algebras there are precisely five isomorphism classes.…

In this paper, we give a classification of the 3-dimensional associative algebras over the complex numbers, including a construction of the moduli space, using versal deformations to determine how the space is glued together.

Pfaffians of matrices with entries z[i,j]/(x\_i+x\_j), or determinants of matrices with entries z[i,j]/(x\_i-x\_j), where the antisymmetrical indeterminates z[i,j] satisfy the Pl\"ucker relations, can be identified with a trace in an…

By algebraic group theory, there is a map from the semisimple conjugacy classes of a finite group of Lie type to the conjugacy classes of the Weyl group. Picking a semisimple class uniformly at random yields a probability measure on…

We reduce the classification of finite subgroups in compact Lie groups to that of quasi-simple ones, prove the number of conjugacy classes is finite and each cojugacy class is Zariski closed in mapping space, and classify "strongly…

We present a Langlands dual realization of the putative category of affine character sheaves. Namely, we calculate the categorical center and trace (also known as the Drinfeld center and trace, or categorical Hochschild cohomology and…

Let $G$ be a closed highly homogeneous subgroup of $S_{\infty}$ not involving circular orderings. We show that the closure of a conjugacy class from $G$ contains a conjugacy class which is comeagre in it. Furthermore, we show that the…

We show that Nichols algebras of most simple Yetter-Drinfeld modules over the projective special linear group over a finite field, corresponding to semisimple orbits, have infinite dimension. We introduce a new criterium to determine when a…

Suppose that $x$, $y$ are elements of a finite group $G$ lying in conjugacy classes of coprime sizes. We prove that $\langle x^G \rangle \cap \langle y^G \rangle$ is an abelian normal subgroup of $G$ and, as a consequence, that if $x$ and…

Several decades ago, John McKay suggested a correspondence between nodes of the affine E8 Dynkin diagram and certain conjugacy classes in the Monster group. Thanks to Monstrous Moonshine, this correspondence can be recast as an assignment…

Let $G$ be an almost simple simply connected group over $\BC$, and let $\Bun^a_G(\BP^2,\BP^1)$ be the moduli scheme of principal $G$-bundles on the projective plave $\BP^2$, of second Chern class $a$, trivialized along a line $\BP^1\subset…

We prove the freeness conjecture of Broue, Malle and Rouquier for the Hecke algebras associated to the primitive complex 2-reflection groups with a single conjugacy class of reflections.