Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

Special Issue on New Directions in Lie Theory

The Guest Editors for this special issue are

Vyjayanthi Chari (University of California, Riverside, USA)
Kailash Misra (North Carolina State University, USA)
Erhard Neher (University of Ottawa, Canada)
Masato Okado (Osaka University, Japan)
Hugh Thomas (University of New Brunswick, Canada)

This special issue of SIGMA features articles by participants of the thematic program “New Directions in Lie Theory”, held at the Centre de Recherches Mathématiques, Montréal, Canada in January–July 2014.

The topics covered come from

  • combinatorial representation theory;
  • Hall and cluster algebras;
  • Lie theory related to mathematical physics;
  • categorification and geometric representation theory.

We would like to thank all the contributors to this special issue and the referees for their careful and insightful reviews. We are also grateful to the Centre de Recherches Mathématique for sponsoring the thematic program.

The Guest Editors        

Papers in this Issue:

$T$-Path Formula and Atomic Bases for Cluster Algebras of Type $D$
Emily Gunawan and Gregg Musiker
SIGMA 11 (2015), 060, 46 pages   [ abs   pdf ]
A Combinatorial Formula for Certain Elements of Upper Cluster Algebras
Kyungyong Lee, Li Li and Matthew R. Mills
SIGMA 11 (2015), 049, 24 pages   [ abs   pdf ]
Cluster Variables on Certain Double Bruhat Cells of Type $(u,e)$ and Monomial Realizations of Crystal Bases of Type A
Yuki Kanakubo and Toshiki Nakashima
SIGMA 11 (2015), 033, 32 pages   [ abs   pdf ]
Skein Modules from Skew Howe Duality and Affine Extensions
Hoel Queffelec
SIGMA 11 (2015), 030, 36 pages   [ abs   pdf ]
The Feigin Tetrahedron
Dylan Rupel
SIGMA 11 (2015), 024, 30 pages   [ abs   pdf ]
Vertex Algebras $\mathcal{W}(p)^{A_m}$ and $\mathcal{W}(p)^{D_m}$ and Constant Term Identities
Dražen Adamović, Xianzu Lin and Antun Milas
SIGMA 11 (2015), 019, 16 pages   [ abs   pdf ]
Irreducible Generic Gelfand-Tsetlin Modules of $\mathfrak{gl}(n)$
Vyacheslav Futorny, Dimitar Grantcharov and Luis Enrique Ramirez
SIGMA 11 (2015), 018, 13 pages   [ abs   pdf ]
On the Killing form of Lie Algebras in Symmetric Ribbon Categories
Igor Buchberger and Jürgen Fuchs
SIGMA 11 (2015), 017, 21 pages   [ abs   pdf ]
Extension Fullness of the Categories of Gelfand-Zeitlin and Whittaker Modules
Kevin Coulembier and Volodymyr Mazorchuk
SIGMA 11 (2015), 016, 17 pages   [ abs   pdf ]
On a Certain Subalgebra of $U_q(\widehat{\mathfrak{sl}}_2)$ Related to the Degenerate $q$-Onsager Algebra
Tomoya Hattai and Tatsuro Ito
SIGMA 11 (2015), 007, 13 pages   [ abs   pdf ]
Bosonizations of $\widehat{\mathfrak{sl}}_2$ and Integrable Hierarchies
Bojko Bakalov and Daniel Fleisher
SIGMA 11 (2015), 005, 19 pages   [ abs   pdf ]
Demazure Modules, Chari-Venkatesh Modules and Fusion Products
Bhimarthi Ravinder
SIGMA 10 (2014), 110, 10 pages   [ abs   pdf ]
Center of Twisted Graded Hecke Algebras for Homocyclic Groups
Wee Liang Gan and Matthew Highfield
SIGMA 10 (2014), 098,  7 pages   [ abs   pdf ]
$\mathcal{A}=\mathcal{U}$ for Locally Acyclic Cluster Algebras
Greg Muller
SIGMA 10 (2014), 094,  8 pages   [ abs   pdf ]
Maximal Green Sequences of Exceptional Finite Mutation Type Quivers
Ahmet I. Seven
SIGMA 10 (2014), 089,  5 pages   [ abs   pdf ]
Schur Positivity and Kirillov-Reshetikhin Modules
Ghislain Fourier and David Hernandez
SIGMA 10 (2014), 058,  9 pages   [ abs   pdf ]
Graded Limits of Minimal Affinizations in Type $D$
Katsuyuki Naoi
SIGMA 10 (2014), 047, 20 pages   [ abs   pdf ]
Tilting Modules in Truncated Categories
Matthew Bennett and Angelo Bianchi
SIGMA 10 (2014), 030, 23 pages   [ abs   pdf ]
Leibniz Algebras and Lie Algebras
Geoffrey Mason and Gaywalee Yamskulna
SIGMA 9 (2013), 063, 10 pages   [ abs   pdf ]

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