Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Coherent systems of probability measures on graphs for representations
  of free Frobenius towers   First formally defined by Borodin and Olshanski, a coherent system on a
graded graph is a sequence of probability measures which respect the action of
certain down/up transition functions between graded components. In one common
example of such a construction, each measure is the Plancherel measure for the
symmetric group $S_{n}$ and the down transition function is induced from the
inclusions $S_{n} \hookrightarrow S_{n+1}$.
  In this paper we generalize the above framework to the case where $\{A_n\}_{n
\geq 0}$ is any free Frobenius tower and $A_n$ is no longer assumed to be
semisimple. In particular, we describe two coherent systems on graded graphs
defined by the representation theory of $\{A_n\}_{n \geq 0}$ and connect one of
these systems to a family of central elements of $\{A_n\}_{n \geq 0}$. When the
algebras $\{A_n\}_{n \geq 0}$ are not semisimple, the resulting coherent
systems reflect the duality between simple $A_n$-modules and indecomposable
projective $A_n$-modules.

15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph