22 citations · 69 across the 16 of their papers we have counts for
9 papers · 1 filter
Cellular bases for algebras with a Jones basic construction
John Enyang, Frederick M. Goodman
We define a method which produces explicit cellular bases for algebras obtained via a Jones basic construction. For the class of algebras in question, our method gives formulas for…
Comparison of Admissibility Conditions for Cyclotomic Birman--Wenzl--Murakami Algebras
Frederick M. Goodman
We show the equivalence of admissibility conditions proposed by Wilcox and Yu and by Rui and Xu for the parameters of cyclotomic BMW algebras.
Admissibility Conditions for Degenerate Cyclotomic BMW Algebras
Frederick M. Goodman
We study admissibility conditions for the parameters of degenerate cyclotomic BMW algebras. We show that the u-admissibility condition of Ariki, Mathas and Rui is equivalent to a s…
Cellularity of Cyclotomic Birman--Wenzl--Murakami algebras
Frederick M. Goodman
We show that the cyclotomic Birman-Wenzl-Murakami algebras are cellular by producing a cellular basis of affine tangle diagrams.
Cyclotomic Birman--Wenzl--Murakami algebras, II: Admissibility Relations and Freeness
Frederick M. Goodman, Holly Hauschild Mosley
The cyclotomic Birman-Wenzl-Murakami algebras are quotients of the affine BMW algebras in which the affine generator satisfies a polynomial relation. We study admissibility conditi…
Cyclotomic Birman--Wenzl--Murakami algebras, I: Freeness and realization as tangle algebras
Frederick M. Goodman, Holly Hauschild Mosley
The cyclotomic Birman-Wenzl-Murakami algebras are quotients of the affine BMW algebras in which the affine generator satisfies a polynomial relation. We show that the cyclotomic BM…
Affine Birman-Wenzl-Murakami Algebras and Tangles in the Solid Torus
Frederick M. Goodman, Holly M. Hauschild
The ordinary (or classical) Birman-Wenzl-Murakami algebras were initially conceived as an algebraic framework for the Kauffman link invariant. They also appear as centralizer algeb…
Ideals in the Temperley Lieb Category
Frederick M. Goodman, Hans Wenzl
We prove the following result: For a generic value of the parameter, the Temperley-Lieb category has no non-zero, proper tensor ideal. When the parameter is equal to $2\cos(π/n…
Crystal Bases of Quantum Affine Algebras and Affine Kazhdan-Lusztig Polynomials
Frederick M. Goodman, Hans Wenzl
We present a fast version of the algorithm of Lascoux, Leclerc, and Thibon for the lower global crystal base for the Fock representation of quantum affine sl_n. We also show that t…