15 citations · 63 across the 17 of their papers we have counts for
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Polystability in positive characteristic and degree lower bounds for invariant rings
Harm Derksen, Visu Makam
We develop a representation theoretic technique for detecting closed orbits that is applicable in all characteristics. Our technique is based on Kempf's theory of optimal subgroups…
Maximum likelihood estimation for matrix normal models via quiver representations
Harm Derksen, Visu Makam
In this paper, we study the log-likelihood function and Maximum Likelihood Estimate (MLE) for the matrix normal model for both real and complex models. We describe the exact number…
Singular tuples of matrices is not a null cone (and, the symmetries of algebraic varieties)
Visu Makam, Avi Wigderson
The following multi-determinantal algebraic variety plays a central role in algebra, algebraic geometry and computational complexity theory: , consisting of all $…
Invariant theory and wheeled PROPs
Harm Derksen, Visu Makam
We study the category of wheeled PROPs using tools from Invariant Theory. A typical example of a wheeled PROP is the mixed tensor algebra , whe…
An exponential lower bound for the degrees of invariants of cubic forms and tensor actions
Harm Derksen, Visu Makam
Using the Grosshans Principle, we develop a method for proving lower bounds for the maximal degree of a system of generators of an invariant ring. This method also gives lower boun…
Weyl's polarization theorem in positive characteristic
Harm Derksen, Visu Makam
Let be an -dimensional algebraic representation over an algebraically closed field of a group . For , we study the invariant rings for the diagon…
Extensions between Verma modules for dihedral groups
Gurbir Dhillon, Visu Makam
Computing the extensions between Verma modules is in general a very difficult problem. Using Soergel bimodules, one can construct a graded version of the principal block of Categor…
Generating invariant rings of quivers in arbitrary characteristic
Harm Derksen, Visu Makam
It is well known that the ring of polynomial invariants of a reductive group is finitely generated. However, it is difficult to give strong upper bounds on the degrees of the gener…
Degree bounds for semi-invariant rings of quivers
Harm Derksen, Visu Makam
We use recent results on matrix semi-invariants to give degree bounds on generators for the ring of semi-invariants for quivers with no oriented cycles.
Polynomial degree bounds for matrix semi-invariants
Harm Derksen, Visu Makam
We study the left-right action of on -tuples of matrices with entries in an infinite field . We show that invari…
Hilbert series and degree bounds for matrix (semi-)invariants
Visu Makam
We study the ring R(n,m) of invariants for the left-right action of SL_n \times SL_n on m-tuples of n by n complex matrices. We show that R(3,m) is generated by invariants of degre…