scholarly journals A DG-extension of symmetric functions arising from higher representation theory

2018 ◽  
Vol 2 (2) ◽  
pp. 169-214
Author(s):  
Andrea Appel ◽  
Ilknur Egilmez ◽  
Matthew Hogancamp ◽  
Aaron Lauda
Keyword(s):  
Representation Theory ◽  
Symmetric Functions

scholarly journals Limits of Modified Higher $q,t$-Catalan Numbers

10.37236/3201 ◽  
2013 ◽  
Vol 20 (3) ◽  
Author(s):  
Kyungyong Lee ◽  
Li Li ◽  
Nicholas A Loehr
Keyword(s):  
Representation Theory ◽  
Symmetric Functions ◽  
Rational Functions ◽  
Catalan Numbers ◽  
Integer Partitions ◽  
Hilbert Schemes ◽  
Intensive Study ◽  
Nabla Operator ◽  
Dyck Paths ◽  
Partition Statistics

The $q,t$-Catalan numbers can be defined using rational functions, geometry related to Hilbert schemes, symmetric functions, representation theory, Dyck paths, partition statistics, or Dyck words. After decades of intensive study, it was eventually proved that all these definitions are equivalent. In this paper, we study the similar situation for higher $q,t$-Catalan numbers, where the equivalence of the algebraic and combinatorial definitions is still conjectural. We compute the limits of several versions of the modified higher $q,t$-Catalan numbers and show that these limits equal the generating function for integer partitions. We also identify certain coefficients of the higher $q,t$-Catalan numbers as enumerating suitable integer partitions, and we make some conjectures on the homological significance of the Bergeron-Garsia nabla operator.

Representation Theory and Harmonic Analysis of Wreath Products of Finite Groups

2009 ◽  
Author(s):  
Tullio Ceccherini-Silberstein ◽  
Fabio Scarabotti ◽  
Filippo Tolli
Keyword(s):  
Representation Theory ◽  
Harmonic Analysis ◽  
Finite Groups ◽  
Wreath Products

On the Positivity of $\mathbf{{a}}$-Linear with Random Finitely

2020 ◽  
Author(s):  
Amanda Bolton
Keyword(s):  
Representation Theory ◽  
Central Problem ◽  
Numerical Representation

Let $\rho$ be an ultra-unique, reducible topos equipped with a minimal homeomorphism. We wish to extend the results of \cite{cite:0} to trivially Cartan classes. We show that $d$ is comparable to $\mathcal{{M}}$. This leaves open the question of uniqueness. Moreover, a central problem in numerical representation theory is the description of irreducible, orthogonal, hyper-unique graphs.

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