1 citations · 3 across the 13 of their papers we have counts for
14 papers
A Kohno--Drinfeld Theorem for iquantum Weyl groups
Elijah Bodish, Ivan Motorin
We prove that two finite-dimensional linear representations of the braid group are isomorphic. One representation comes from the monodromy of the boundary Casimir connection, and t…
Type Webs
Elijah Bodish, Ben Elias, David E. V. Rose
We solve the type case of the main open problem from Kuperberg's 1996 paper "Spiders for rank 2 Lie algebras." That is, we define a -linear pivotal category $\ma…
MOY calculus in type D
Elijah Bodish, Louis-Hadrien Robert, Emmanuel Wagner
We define a positive state sum for webs "of type D". These webs are graphs which mimic morphisms in the category of finite-dimensional quantum so(2N)-modules. From the state sum, w…
Cyclotomic nil-Brauer and Singular Soergel bimodules of type D
Elijah Bodish, Jonathan Brundan, Ben Elias
We introduce a new family of monoidal categories which are cyclotomic quotients of the nil-Brauer category. We construct a monoidal functor from the cyclotomic nil-Brauer category…
Spin Link Homology
Elijah Bodish, Ben Elias, David E. V. Rose
We put a new spin on Khovanov--Rozansky homology. That is, we equip -colored Khovanov--Rozansky homology with an involution whose -eigenspaces are…
Orthogonal Howe duality and dynamical (split) symmetric pairs
Elijah Bodish, Artem Kalmykov
Inspired by Etingof--Varchenko's dynamical fusion, dynamical -matrix, and dynamical Weyl group for Lie algebras, we introduce, for split symmetric pairs, versions of dynamical f…
Orthogonal webs and semisimplification
Elijah Bodish, Daniel Tubbenhauer
We define a diagrammatic category that is equivalent to tilting representations for the orthogonal group. Our construction works in characteristic not equal to two. We also describ…
Webs for the Quantum Orthogonal Group
Elijah Bodish, Haihan Wu
We give a generators and relations presentation for the full monoidal subcategory of representations of the quantum orthogonal group generated by the quantum exterior powers of the…
On a symplectic quantum Howe duality
Elijah Bodish, Daniel Tubbenhauer
We prove a nonsemisimple quantum version of Howe's duality with the rank 2n symplectic and the rank 2 special linear group acting on the exterior algebra of type C. We also discuss…
Triple Clasp Formulas for
Elijah Bodish, Haihan Wu
We use Kuperberg's diagrammatic description of the space of homomorphisms between fundamental representations of to give explicit recursive formulas for the idempotent projec…
Decreasing subsequences and Viennot for oscillating tableaux
Elijah Bodish, Ben Elias, David E. V. Rose +1
We establish an extension of Viennot's geometric (shadow line) construction to the setting of oscillating tableaux. We then use this to give a new proof of the Type analogue of…
Type Webs
Elijah Bodish, Ben Elias, David E. V. Rose +1
We define a -linear pivotal category and prove that it is equivalent to the full subcategory of finite-dimensional representations…
Triple clasp formulas for webs
Elijah Bodish
Using the light ladder basis for Kuperberg's webs, we derive triple clasp formulas for idempotents projecting to the top summand in each tensor product of fundamental represe…
Web Calculus and Tilting Modules in Type
Elijah Bodish
Using Kuperberg's webs, and following Elias and Libedinsky, we describe a "light leaves" algorithm to construct a basis of morphisms between arbitrary tensor products of…