24 citations · 54 across the 25 of their papers we have counts for
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Invariant differential derivations for reflection groups in positive characteristic
Anne V. Shepler, Dillon Hanson
Much of the fascinating numerology surrounding finite reflection groups stems from Solomon's celebrated 1963 theorem describing invariant differential forms. Invariant differential…
Invariant theory for coincidental complex reflection groups
Victor Reiner, Anne V. Shepler, Eric Sommers
V.F. Molchanov considered the Hilbert series for the space of invariant skew-symmetric tensors and dual tensors with polynomial coefficients under the action of a real reflection g…
Invariants of polynomials mod Frobenius powers
C. Drescher, A. V. Shepler
Lewis, Reiner, and Stanton conjectured a Hilbert seriesfor a space of invariants under an action of finite general linear groups using -binomial coefficients. This work give…
Steinberg's theorem for crystallographic complex reflection groups
Philip Puente, Anne V. Shepler
Popov classified crystallographic complex reflection groups by determining lattices they stabilize. These analogs of affine Weyl groups have infinite order and are generated by ref…
Invariant derivations and differential forms for reflection groups
Victor Reiner, Anne V. Shepler
Classical invariant theory of a complex reflection group highlights three beautiful structures: -- the -invariant polynomials constitute a polynomial algebra, over which --…
Group Coding with Complex Isometries
Hye Jung Kim, J. B. Nation, Anne V. Shepler
We investigate group coding for arbitrary finite groups acting linearly on a vector space. These yield robust codes based on real or complex matrix groups. We give necessary and su…