Professor of Mathematics, Stanford University

Daniel Bump's research is in representation theory.

- Crystal Bases: Representations and Combinatorics with Anne Schilling. Errata for this book.
- Weyl Group Multiple Dirichlet Series: Type A Combinatorial Theory with Brubaker and Friedberg.
- Multiple Dirichlet Series, L-functions and Automorphic Forms, Bump, Friedberg and Goldfeld (ed.), Birkhauser Prog. Math. 300 (2012)
- Lie Groups, Springer GTM volume 225. The second edition appeared in 2013.
- Automorphic Forms and Representations, published by Cambridge University Press. Here is a list of errata, some of which were corrected in the paperback edition.
- Algebraic Geometry, published by World Scientific.

Email me if you find any broken links.

- Matrix Coefficients of intertwining operators and the Bruhat Order, with Beatrice Chetard.
- Metaplectic Iwahori Whittaker functions and supersymmetric lattice models, with Brubaker, Buciumas and Gustafsson.
- Colored Lattice Models and Iwahori Whittaker Functions, with Brubaker, Buciumas and Gustafsson.
- Colored 5-vertex models and Demazure Atoms, with Brubaker, Buciumas and Gustafsson. In J. Combinatorial Theory A.
- Vertex operators, solvable lattice models and metaplectic Whittaker functions, with Brubaker, Buciumas and Gustafsson. In Communications in Mathematical Physics.
- Casselman's basis of Iwahori vectors and Kazhdan-Lusztig polynomials with Maki Nakasuji. Canad. J. Math. 71 (2019), no. 6, 1351
- Duality for Metaplectic Ice with Buciumas, Brubaker and Gray. A version of this appeared as an appendix to "A Yang-Baxter equation for metaplectic ice" in Communications in Number Theory and Physics.
- Hecke Modules from Metaplectic Ice with Brubaker, Buciumas and Friedberg. Selecta Math. 24 (2018), no. 3, 2523.
- A Yang-Baxter equation for Metaplectic Ice with Brubaker and Buciumas. Commun. Number Theory Phys. 13 (2019), no. 1, 101
- Bump, Diaconis, Hicks and Widom, An Exercise (?) in Fourier Analysis on the Heisenberg Group, Ann. Fac. Sci. Toulouse Math. (6) 26 (2017), no. 2, 263
- Bump, Diaconis, Hicks and Widom, Useful bounds on the extreme eigenvalues and vectors of matrices for Harper's operators, In Large truncated Toeplitz matrices, Toeplitz operators, and related topics.
- Matrix Coefficients and Iwahori-Hecke algebra modules with Brubaker and Friedberg. Adv. Math. 299 (2016), 247.
- Unique Functionals and Representations of Hecke Algebras. With Brubaker and Friedberg, dedicated to Jonathan Rogawski. Pacific J. Math. 260 (2012), no. 2, 381.
- Multiple Dirichlet Series. In the book Multiple Dirichlet Series, L-functions and Automorphic Forms, Bump, Friedberg and Goldfeld (ed.), Birkhauser Prog. Math. 300 (2012).
- Schubert Eisenstein Series with Young-Ju Choie. Amer. J. Math. 136 (2014), no. 6, 1581
- Factorial Schur Functions and the Yang-Baxter Equation with McNamara and Nakasuji. Comment. Math. Univ. St. Pauli 63 (2014). Dedicated to Fumihiro Sato.
- Whittaker Functions and Demazure Operators with Brubaker and Licata. (Dedicated to Steve Rallis). Whittaker functions and Demazure operators. J. Number Theory 146 (2015), 41
- Eisenstein Series, Crystals and Ice with Brubaker and Friedberg
- Metaplectic Ice with Brubaker, Chinta, Friedberg and Gunnells. In the book Multiple Dirichlet Series, L-functions and Automorphic Forms, Bump, Friedberg and Goldfeld (ed.), Birkhauser Prog. Math. 300 (2012)
- Crystals of Type B and Metaplectic Whittaker Functions with Brubaker, Chinta, and Gunnells. In the book Multiple Dirichlet Series, L-functions and Automorphic Forms, Bump, Friedberg and Goldfeld (ed.), Birkhauser Prog. Math. 300 (2012)
- Coefficients of the n-fold theta function with Brubaker, Friedberg and Hoffstein. Dedicated to S. J. Patterson. In Contributions in analytic and algebraic number theory (2012).
- The Casselman Basis of Iwahori Fixed Vectors and the Bruhat Order with Nakasuji. In the Canadian J. of Mathematics.
- Schur Polynomials and the Yang-Baxter Equation with Brubaker and Friedberg. To appear in Comm. Math. Phys. Comm. Math. Phys. 308 (2011), no. 2, 281
- Integration on p-adic groups and Crystal bases with Maki Nakasuji. In Proceedings of the AMS.
- Weyl Group Multiple Dirichlet Series, Eisenstein Series and Crystal Bases, with Ben Brubaker and Solomon Friedberg. To appear in Annals of Mathematics.
- Weyl Group Multiple
Dirichlet Series: Type A Combinatorial Theory, with Ben Brubaker and
Solomon Friedberg.
**Preprint version.**The published version is Annals of Mathematics Studies 175, which contains more expository material than this preprint version. - Gauss Sum Combinatorics and Metaplectic Eisenstein series, with Ben Brubaker and Solomon Friedberg.
- Weyl Group Multiple Dirichlet Series I, with Brubaker, Chinta, Friedberg and Hoffstein.
- Weyl Group Multiple Dirichlet Series II: The Stable Case , with Ben Brubaker and Solomon Friedberg. To appear in Inventiones Math.
- Weyl Group Multiple Dirichlet Series III: Eisenstein Series and Twisted Unstable Ar, with Ben Brubaker, Solomon Friedberg and Jeffrey Hoffstein. And here are two companion papers. The first, Metaplectic Eisenstein Series on GL(3) contains two articles with more details about some of the proofs. The second, Gelfand-Tsetlin interpretation of Chinta's A5 polynomial is only available as a TeX dvi file since this is a smaller format than postscript or pdf. You should not print it since it is very long.
- Residues of Weyl Group Multiple Dirichlet Series Associated to GL(n + 1) with Ben Brubaker.
- Weyl Group Multiple Dirichlet Series IV: The stable twisted case with Ben Brubaker and Solomon Friedberg.
- On Kubota's Dirichlet Series (postscript file), with Ben Brubaker. Here's the same paper as a PDF file.
- Unraveling the (miniature) Rubik's cube through it's Cayley Graph with Dan Auerbach.
- On derivatives of modular forms of negative weight, with YoungJu Choie. To appear in the Pure and Applied Mathematics Quarterly, dedicated to John Coates.
- On the Averages of Characteristic Polynomials from Classical Groups, with Alex Gamburd. To appear in Communications in Mathematical Physics.
- A Summation Formula for Divisor Functions Associated to Lattices with Jennifer Beineke. (To appear in Forum Math.) Here's the Appendix which will become obsolete when Professor Sato's paper appears.
- Lifting Automorphic Representations on Double Covers of Orthogonal Groups with Friedberg and Ginzburg. (To appear in Duke Math. J.) Here's a PDF version.
- The Rankin Selberg Method: An Introduction and Survey. (To appear in the volume dedicated to Steve Rallis.)
- Generalized Frobenius Schur Numbers with David Ginzburg (In Journal of Algebra 278).
- Small representations for Odd Orthogonal Groups with Friedberg and Ginzburg (In IMRN 25).
- Moments of the Riemann Zeta Function and Eisenstein Series I with Jennifer Beineke (in Journal of Number Theory).
- Moments of the Riemann Zeta Function and Eisenstein Series II with Jennifer Beineke (in Journal of Number Theory).
- The last two papers supercede ``Moments of L-functions of Maass forms and the Riemann zeta function'' with Jennifer Beineke.
- Renormalized periods on GL(3) with Jennifer Beineke. In the Canadian Journal of Mathematics.
- Spectral Theory and the Trace Formula. Here's the (preliminary) revised version.
- Sums of twisted GL(3) automorphic L-functions joint with Friedberg and Hoffstein. To appear in a volume dedicated to Joseph Shalika.
- On the dimension of the space of theta functions joint with Alex Pekker. Based on Alex' senior thesis. To appear in Proceedings of the AMS.
- An L-function of degree 27 for Spin(9), joint with Ginzburg. A short version will appear in the Ramanujan Journal.
- A Rankin-Selberg Integral using The Automorphic Minimal Representation of SO(7) by Bump, Friedberg and Ginzburg. This has appeared in the Journal of the Ramanujan Math. Society.
- On the cubic Shimura lift for PGL(3), with Friedberg and Ginzburg. This appeared in the Israel Journal of Mathematics.
- Hidden symmetries for a renormalized integral of Eisenstein series, with Jennifer Beineke. This appeared in Forum Math.
- Whittaker-Fourier Coefficients of Metaplectic Eisenstein Series with William Banks and Daniel Lieman. To appear in Compositio Math.
- Toeplitz minors, with Persi Diaconis. This appeared in the Journal of Combinatorial Theory A.
- Correction to Toeplitz minors as a postscript file and a dvi file.
- Unitary Correlations and the Fejer kernel, with Persi Diaconis and Joseph B. Keller. This appeared in Mathematical Physics, Analysis and Geometry.

- Zurich 2018. Vertex Operators and Metaplectic Whittaker Functions (arXiv:1806.07776)
- Utah 2016. From Whittaker Functions to Quantum Groups.
- Class web page for 2015's Math 263B (Modular Representation Theory)
- Notes on Crystals
- Goldfeld Conference (2007) Gauss Sum Combinatorics and Multiple Dirichlet Series.
- New York, 2011. Crystals and Multiple Dirichlet Series
- Montreal 2014. Metaplectic Ice and the Combinatorics of Whittaker Functions.
- Banff 2013. Whittaker Functions and Quantum Groups.
- Davis 2013. Introduction to Git.
- Lie Methods and Related Combinatorics in Sage by Bump and Schilling
- Whittaker Functions, 2010.
- Group Representation Theory, notes for an undergraduate course.
- Hecke Algebras

- Rubik cube notes
- Materials for a previous course on class field theory are here.
- A lecture given in Rochester in June 2006.
- A lecture in honor of Steve Gelbart given in Tel Aviv in May 2006.
- Slides for a in Bretton Woods on Weyl Group Multiple Dirichlet Series.
- Theta Representations of Odd Orthogonal Groups, slides of a talk to be given in Exeter on September 18, 2004, based on work of Bump, Friedberg and Ginzburg.
- Automorphic Summation Formulae and Moments of Zeta, based on work of Beineke and Bump.
- The Lang Map.
- Twisted Conjugacy.
- Notes on Representations of GL(r) over a Finite Field. Very Old Notes.
- Brauer Characters and Green's Theorem
- Construction of cusp forms.
- Shintani's Theorem.
- Orbital Integrals and the Satake Isomorphism.
- The Plancherel Formula for Math 249b.
- The Selberg Zeta Function for Math 249b.
- The Explicit Formula for Math 249b.
- Some set theory. (Originally for Math 210.)
- Here is some material Riemann zeta function,
- Maxwell's Equations, lecture notes form Math 52 (Vector Calculus). A postscript file.
- Coulomb Force and Potential, lecture notes form Math 52 (Vector Calculus). A postscript file. left over from a graduate course.

- Bretton Woods Workshop on Multiple Dirichlet Series.
- Stanford Workshop on Multiple Dirichlet Series.

- TeXmacs is a better way of writing mathematics.
- Sage, the computer algebra system, is excellent and rapidly developing.

Back to Stanford Math Department.

`email:`bump at math dot stanford dot edu