Representability of the direct sum of uniform q-matroids

There are many similarities between the theories of matroids and q-matroids. However, when dealing with the direct sum of q-matroids many differences arise. Most notably, it has recently been shown that the direct sum of representable q-matroids is not necessarily representable. In this work, we focus on the direct sum of uniform q-matroids. Using algebraic and geometric tools, together with the notion of cyclic flats of q-matroids, we show that this is always representable, by providing a representation over a sufficiently large field.