7 papers
A field-independent filtration of plethystic modules for that categorifies a product rule for the Cartan subalgebra of
Ãlvaro Gutiérrez, Ãlvaro L. MartÃnez, MichaÅ Szwej +1
We lift a product rule in the Cartan subalgebra of quantum to a filtration of the plethystic representation of the affine group schem…
Modular isomorphisms of -plethysms for Weyl modules labelled by hook partitions
Ãlvaro Gutiérrez, Ãlvaro L. MartÃnez, MichaÅ Szwej +1
Let be the Weyl functor for the partition and let be the natural -dimensional representation of , where is an arbitrary…
Quantum computation and quantum error correction: the theoretical minimum
Mark Wildon
These notes introduce quantum computation and quantum error correction, emphasising the importance of stabilisers and the mathematical foundations in basic Lie theory. We begin by…
FrontierMath: A Benchmark for Evaluating Advanced Mathematical Reasoning in AI
Elliot Glazer, Ege Erdil, Tamay Besiroglu +21
We introduce FrontierMath, a benchmark of hundreds of original, exceptionally challenging mathematics problems crafted and vetted by expert mathematicians. The questions cover most…
A new bijective proof of the -Pfaff--Saalschütz identity with applications to quantum groups
Ãlvaro Gutiérrez, Ãlvaro L. MartÃnez, MichaÅ Szwej +1
We present a combinatorial proof of the -Pfaff--Saalschütz identity by a composition of explicit bijections, in which -binomial coefficients are interpreted as counting subs…
Two stability theorems on plethysms of Schur functions
Rowena Paget, Mark Wildon
The plethysm product of Schur functions corresponds to composing polynomial representations of infinite general linear groups. Finding the plethysm coefficients $\langle s_ν\circ…