Weakly commensurable arithmetic groups and isospectral locally symmetric spaces

By Gopal Prasad, A. Rapinchuk. 2007

114 citations recorded by the source corpus.

We introduce the notion of weak commensurabilty of arithmetic subgroups and relate it to the length equivalence and isospectrality of locally symmetric spaces. We prove many strong consequences of weak commensurabilty and derive from these many interesting results about isolength and isospectral locally symmetric spaces.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/65bfe97a1354228a85a5de309ac94d9da630471f

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In Discrete Mathematics and Combinatorics

1. L. Funar
2. Gopal Prasad
3. A. Rapinchuk

In Geometry and Topology

1. L. Funar
2. Gopal Prasad
3. A. Rapinchuk
4. Gareth Wilkes
5. Henry Wilton
6. Pavel A. Zalesskii
7. JongHae Keum

In Mathematical Physics

1. L. Funar
2. A. Rapinchuk
3. Gopal Prasad
4. Gareth Wilkes
5. Henry Wilton
6. Pavel A. Zalesskii

Citations in the corpus

• Local-global principles for embedding of fields with involution into simple algebras with involution (2008, methodology): “…with involution (E, σ), or for a particular class of central simple algebras with involution (A, τ)) if the existence of (L⊗K Kv)-embeddings ιv : (E ⊗K Kv , σ ⊗ idKv) →֒ (A⊗K Kv, τ ⊗ idKv) for all v ∈ V K (here V K denotes the set of all places of K) implies the existence of an L-embedding…”
• Torus bundles not distinguished by TQFT invariants (2011, methodology): “d by taking arbitrary lifts ˜x ∈ (Z/2kZ)n and setting qTxA Lx = q TxA˜ Lx˜, which is independent on the choice of the lifts, since A is symmetric. These invariants where further extended by Deloup in [10] by making use of general quadratic forms and finally extended to TQFTs in [11]. These TQFT corre”