# Research and Publications

My interests are in algebra and operator algebras. The following is a list of recent publications. My full publication list is here.

John Enyang and F.M. Goodman, The seminormal representations of the Brauer algebra, in preparation, preliminary version .

Christopher Bowman, John Enyang, and F.M. Goodman, Diagram algebras, dominance triangularity, and skew cell modules, to appear in Journal of the Australian Mathematical Society , arXiv:1610.09010 .

Christopher Bowman, John Enyang, and F.M. Goodman, The cellular second fundamental theorem of invariant theory for classical groups, to appear in International Mathematics Research Notices , arXiv:1610.09009 .

F. M. Goodman, Ross Kilgore, and Nicholas Teff, A cell filtration of the restriction of a cell module, preprint (2015), arXiv:1504.02136.

J. Enyang and F.M. Goodman, Cellular bases for algebras with a Jones basic construction, Algebras and Representation Theory 20 (2017) 71–121; DOI: 10.1007/s10468-016-9632-5.

T. Geetha and F.M. Goodman, Cellularity of Wreath Product Algebras and $A$--Brauer algebras, Journal of Algebra 389 (2013) 151–190; preprint version: arXiv:1208.2983.

F.M. Goodman, Remarks on cyclotomic and degenerate cyclotomic BMW algebras, Journal of Algebra 364 (2012) 13–37; preprint version: arXiv:1011.3284.

F.M. Goodman and John Graber, On cellular algebras with Jucys--Murphy elements, Journal of Algebra 330 (2011) 147-176; preprint version: arXiv:0907.3459.

F.M. Goodman and John Graber, Cellularity and the Jones basic construction, Advances in Applied Mathematics  46 (2011) 312-362; preprint verson: arXiv:0906.1496.

F.M. Goodman, Comparison of admissibility conditions for cyclotomic Birman--Wenzl--Murakami algebras   Journal of Pure and Applied Algebra 214 (2010) 2009–2016; preprint version:  arXiv:0905.4258.

F.M. Goodman, Admissibility conditions for degenerate cyclotomic BMW Algebras, Communications in Algebra 39 (2011) 452-461; preprint version: arXiv:0905.4253.

F.M. Goodman, Cellularity of Cyclotomic Birman--Wenzl--Murakami algebras, Journal of Algebra 321 (2009) 3299-3320; preprint version: arXiv:0801.0306.

F.M. Goodman and Holly Hauschild Mosley, Cyclotomic Birman-Wenzl-Murakami algebras II: Admissibility relations and freeness, Algebras and Representation Theory 14 (2011) 1-39; preprint version: math.QA/0612065.

F.M. Goodman and Holly Hauschild Mosley, Cyclotomic Birman-Wenzl-Murakami algebras I: Freeness and realization as tangle algebras, J. Knot Theory and Ramifications 18 (2009) 1089-1127; preprint version: math.QA/0612064.

F. M. Goodman and H. Hauschild, Affine Birman-Wenzl-Murakami algebras and tangles in the solid torus, Fundamenta Mathematicae 190 (2006) 77-137; preprint version: math.QA/0411155.

F. M. Goodman , Zn--graded independence, Indiana University Mathematics Journal 53 (2004) 515-532; preprint version: math.OA/0206296.

Philippe Biane, F. M. Goodman, and Alexandru Nica, Non-crossing cumulants of type B, Trans. Am. Math. Soc. 355 (2003) 2263-2303; preprint version: math.OA/0206167.

F. M. Goodman and Hans Wenzl, Ideals in the Temperley-Lieb Category, an appendix to Michael Freedman, A magnetic model with a possible Chern-Simons phase, Comm. Math. Phys. 234 (2003) pp 129-183; preprint version: math.QA/0206301.

F. M. Goodman and Hans Wenzl, A path algorithm for affine Kazhdan-Lusztig polynomials, Math. Z. 237 (2001), no. 2, 235--249; preprint version: math.RT/0011245.