7. Martirosyan, L., Wenzl, H.. Braid rigidity for path algebras. Indiana University Mathematics Journal , 71 No. 4 (2022), 1649–1674
ABSTRACT. Path algebras are a convenient way of describing decompositions of tensor powers of an object in a tensor category. If the category is braided, one obtains representations of the braid groups Bn for all n ∈ N. We say that such representations are rigid if they are determined by the path algebra and the representations of B2. We show that besides the known classical cases also the braid representations for the path algebra for the 7-dimensional representation of G2 satisfy the rigidity condition, provided B3 generates End(V ⊗3 ). We obtain a complete classification of ribbon tensor categories with the fusion rules of g(G2) if this condition is satisfied.
6. Martirosyan, L., Moree, P. . Large absolute values of cyclotomic polynomials at roots of unity, Journal of Number Theory, Vol. 239, pages 251-272, (2022), issn = {0022-314X},
ABSTRACT= The nth cyclotomic polynomial Φn(X) is the minimal polynomial of ζn:=e2πi/n. Given an integer m≥1 and a prescribed set S of arithmetic progressions modulo m, we define nx as the product of the primes p≤x lying in those progressions. Let d(n) denote the number of divisors of n. It turns out that under certain conditions on S and m there exists jx such that log|Φnx(ζmjx)|/d(nx) tends to a positive limit. Our aim is to determine those conditions. We use the arithmetic of cyclotomic number fields, non-standard properties of character tables of finite abelian groups and a recent theorem of Bzdȩga, Herrera-Poyatos and Moree. After developing some generalities, we restrict to the case where m is a prime. Our motivation comes from a paper of Vaughan (1975). He studied the case where S={±2(mod5)} and used it to show that the maximum coefficient in absolute value of Φn can be very large.
5. Jones*, G. , Kester*, P. I., Martirosyan, L., Moree. P., Toth, L. , White*, B. B., Zhang, B. (2020). Coefficients of (inverse) unitary cyclotomic polynomials. Kodai Mathematical Journal, Tokyo Institute of Technology, 2020; Vol 43(2); Pages 325-338.
4. A. de Clercq, F. Luca, Martirosyan, L., M. Matthis, P. Moree, M.A. Stoumen* and M. Weiß. (2020).
Binary Recurrences for which Powers of Two are Discriminating Moduli.
Journal of Integer Sequences, Vol. 23 (2020), Article 20.11.3
3. Martirosyan, L., Wenzl, H. (2019). Affine Centralizer Algebras for G2.
International Mathematics Research Notices, Oxford University Press., Vol. 2019, No. 12, pp 3812–3831.
2. Martirosyan, L. (2014). The representation theory of the exceptional Lie superalgebras F(4) and G(3).
Journal of Algebra, Volume 419, ISSN 0021-8693, Pages 167-222.
Martirosyan, L. (2013). The representation theory of the exceptional Lie superalgebras F(4) and G(3).
Thesis (Ph.D.)–University of California, Berkeley. 2013. 110 pp. ISBN: 978-1303-37399-2 ProQuest LLC
*UNCW students