The F-singularities of algebras defined by permanents

Let X be a matrix of indeterminates, t an integer, and Pₜ(X) define the ideal generated by the permanents of all t× t submatrix of X. Pₜ(X) is called a permanental ideal. In this article, we study the algebras [X]/Pₜ(X) where X is a generic, symmetric, or a Hankel matrix of indeterminates. When char = 2, Pₜ(X) is also known as a determinantal ideal, a popular class in commutative algebra and algebraic geometry, and thus many properties of Pₜ(X) are known in this case. We prove that, if X is an n× n matrix and char >2, the algebra [X]/Pₙ(X) is F-regular, just like when char = 2. On the other hand, we obtain a full characterization of when [X]/P₂(X) is F-pure or F-regular, when char >2, and the answer is different than that in even characteristic.