The order of the automorphism group of a binary qq-analog of the Fano plane is at most two

It is shown that the automorphism group of a binary $q$-analog of the Fano plane is either trivial or of order $2$.Comment: 10 page

The Shilov boundary for a qq-analog of the holomorphic functions on the unit ball of 2×22 \times 2 symmetric matrices

We describe the Shilov boundary for a $q$-analog of the algebra of holomorphic functions on the unit ball in the space of symmetric $2 \times 2$ matrices.Comment: 14 page

A q-analog of Ljunggren's binomial congruence

We prove a $q$-analog of a classical binomial congruence due to Ljunggren which states that $$\binom{a p}{b p} \equiv \binom{a}{b}$$ modulo $p^3$ for primes $p\ge5$. This congruence subsumes and builds on earlier congruences by Babbage, Wolstenholme and Glaisher for which we recall existing $q$-analogs. Our congruence generalizes an earlier result of Clark.Comment: 6 pages, to be published in the proceedings of FPSAC 201

On a q-analog of a Sahi result

We obtain a $q$-analog of a well known Sahi result on the joint spectrum of $S(GL_n \times GL_n)$-invariant differential operators with polynomial coefficients on the vector space of complex $n \times n$-matrices.Comment: 9 pages, some improvements in exposition have been mad

Shilov boundary for "holomorphic functions" on a quantum matrix ball

We describe the Shilov boundary ideal for a q-analog of algebra of holomorphic functions on the unit ball in the space of $2\times 2$ matrices.Comment: 14 page