Searcharxiv⌕ Search

arXiv · 0706.1655

Pascal's triangle and word bases for blob algebra ideals

Abstract

We give an elementary proof of isomorphism of the blob (diagram) algebra and the corresponding extended Temperley-Lieb algebra (defined by presentation).

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

P P Martin. 2007-06-12. Pascal's triangle and word bases for blob algebra ideals. https://arxiv.org/abs/0706.1655

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Projection formulas and a refinement of Schur--Weyl--Jones duality for symmetric groups

Schur--Weyl--Jones duality establishes the connection between the commuting actions of the symmetric group $S_{n}$ and the partition algebra $P_{k}(n)$ on the tensor space $\left(\mathbb{C}^n\right)^{\otimes k}.$ We use a refinement of this considered first by Littlewood and later, by Sam and Snowden, whereby there is a version of Schur--Weyl duality for the symmetric groups $S_{n}$ and $S_{k}$ acting on a subspace of $\left(\mathbb{C}^n\right)^{\otimes k}$. We obtain an explicit formula for the orthogonal projection from $\left(\mathbb{C}^n\right)^{\otimes k}$ to each irreducible subrepresentation, yielding a new combinatorial approach to computing stable irreducible characters of the symmetric group.

math.RT↗

On the twisted Osborne conjecture

We aim to prove a twisted version of the Osborne conjecture. The untwisted case was proved by Hecht and Schmid in their 1983 Acta Mathematica paper. Bergeron and Clozel (2013) have considered a special case, and we generalize their method to our setting.

math.RT↗

On the full set of unitarizable supermodules over $\mathfrak{sl}(m\vert n)$

We classify all simple unitarizable supermodules over special linear Lie superalgebras using the algebraic Dirac operator introduced by Huang and Pandžić and the associated Dirac inequalities. The same argument treats finite-dimensional and infinite-dimensional supermodules without requiring explicit realizations or complete branching rules.

math.RT↗